T'ai Chi said:
Could you be kind enough to show me exactly where, with the exact wording, Hahnemann said that 'homeopathy is dealing with dilutions greater than or equal to 6x' ?
In any case, as I've said, I simply did a search for the string 'homeopathy', and reported on what came up. Also, you keep focusing on 1 study where they had 1X, 2X, and 3X dilutions (although it also had a 6X). There are other studies that I posted links to...

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If you want to argue in favor of homeopathy, you really should read the Organon of Medicine by Hahnemann. There are links on the internet to English translations. But since you asked, here's his writings on two pertinent topics: (1) the dilution process he used to get to the minimal concentration he started with (3C which is equivalent to 6X), a (2) how he clearly states that only single remedies can be used at one time (which clearly invalidate the so-called homeopathic products you linked that contain multiple remedies).
Hang on, it's a little long...
"§ 270 Fifth Edition
Thus two drops of the fresh vegetable juice mingled with equal parts of alcohol are diluted with ninety-eight drops of alcohol and potentized by means of two succussions, whereby the first development of power is formed and this process is repeated through twenty-nine more phials, each of which is
filled three-quarters full with ninety-nine drops of alcohol, and each succeeding phial is to be provided with one drop from the preceding phial (which has already been shaken twice) and is in its turn twice shaken,1 and in the same manner at last the thirtieth development of power (potentized
decillionth dilution X) which is the one most generally used.
1 In order to maintain a fixed and measured standard for developing the power of liquid medicines, multiplied experience and careful observation have
led me to adopt two succussions for each phial, in preference to the greater number formerly employed (by which the medicines were too highly
potentized). There are, however, hom?opathists who carry about with them on their visits to patients hom?opathic medicines in the fluid state, and who
yet assert that they do not become more highly potentized in the course of time, but they thereby show their want of ability to observe correctly. I
discovered a grain of soda in half an once of water mixed with alcohol in a phial, which was thereby filled two-thirds full, and shook this solution
continuously for half an hour, and this fluid was in potency and energy equal to the thirtieth development of power.
§ 270 Sixth Edition
In order to best obtain this development of power, a small part of the substance to be dynamized, say one grain, is triturated for three hours with
three times one hundred grains sugar of milk according to the method described below 1 up to the one-millionth part in powder form. For reasons given
below (b) one grain of this powder is dissolved in 500 drops of a mixture of one part of alcohol and four parts of distilled water, of which one drop
is put in a vial. To this are added 100 drops of pure alcohol 2 and given one hundred strong succussions with the hand against a hard but elastic
body.3 This is the medicine in the first degree of dynamization with which small sugar globules 4 may then be moistened 5 and quickly spread on
blotting paper to dry and kept in a well-corked vial with the sign of (I) degree of potency. Only one 6 globule of this is taken for further
dynamization, put in a second new vial (with a drop a water in order to dissolve it) and then with 100 powerful succussions.
With this alcoholic medicinal fluid globules are again moistened, spread upon blotting paper and dried quickly, put into a well-stoppered vial and
protected from heat and sun light and given the sign (II) of the second potency. And in this way the process is continued until the twenty-ninth is
reached. Then with 100 drops of alcohol by means of 100 succussions, an alcoholic medicinal fluid is formed with which the thirtieth dynamization
degree is given to properly moistened and dried sugar globules.
By means of this manipulation of crude drugs are produced preparations which only in this way reach the full capacity to forcibly influence the
suffering parts of the sick organism. In this way, by means of similar artificial morbid affection, the influence of the natural disease on the life
principle present within is neutralized. By means of this mechanical procedure, provided it is carried out regularly according to the above teaching,
a change is effected in the given drug, which in its crude state shows itself only as material, at times as unmedicinal material but by means of such
higher and higher dynamization, it is changed and subtlized at last into spirit-like 7 medicinal power, which, indeed, in itself does not fall within
our senses but for which the medicinally prepared globule, dry, but more so when dissolved in water, becomes the carrier, and in this condition,
manifests the healing power of this invisible force in the sick body.
§ 271 Sixth Edition
If the physician prepares his hom?opathic medicines himself, as he should reasonably do in order to save men from sickness,1 he may use the fresh
plant itself, as but little of the crude article is required, if he does not need the expressed juice perhaps for purposes of healing. He takes a few
grains in a mortar and with 100 grains sugar of milk three distinct times brings them to the one-millionth trituration (§ 270) before further
potentizing of a small portion of this by means of shaking is undertaken, a procedure to be observed also with the rest of crude drugs of either dry
or oily nature.
1 Until the State, in the future, after having attained insight into the indispensability of perfectly prepared hom?opathic medicines, will have them
manufactured by a competent impartial person, in order to give them free of charge to hom?opathic physicians trained in hom?opathic hospitals, who
have been examined theoretically and practically, and thus legally qualified. The physician may then become convinced of these divine tools for
purposes of healing, but also to give them free of charge to his patients - rich and poor.
§ 272 Fifth Edition
In no case is it requisite to administer more than one single, simple medicinal substance at one time.1
1 Some hom?opathists have made the experiment, in cases where they deemed one remedy hom?opathically suitable for one portion of the symptoms of a
case of disease, and a second for another portion, of administering both remedies at the same time; but I earnestly deprecate such a hazardous
experiment, which can never be necessary, though it may sometimes seem to be of use.
§ 272 Sixth Edition
Such a globule,1 placed dry upon the tongue, is one of the smallest doses for a moderate recent case of illness. Here but few nerves are touched by
the medicine. A similar globule, crushed with some sugar of milk and dissolved in a good deal of water (§ 247) and stirred well before every
administration will produce a far more powerful medicine for the use of several days. Every dose, no matter how minute, touches, on the contrary, many
nerves.
1 These globules (§ 270) retain their medicinal virtue for many years, if protected against sunlight and heat.
§ 273 Fifth Edition
It is not conceivable how the slightest dubiety could exist as to whether it was more consistent with nature and more rational to prescribe a single
well-known medicine at one time in a disease, or a mixture of several differently acting drugs.
§ 273 Sixth Edition
In no case under treatment is it necessary and therefore not permissible to administer to a patient more than one single, simple medicinal substance
at one time. It is inconceivable how the slightest doubt could exist as to whether it was more consistent with nature and more rational to prescribe a
single, simple1 medicine at one time in a disease or a mixture of several differently acting drugs. It is absolutely not allowed in hom?opathy, the
one true, simple and natural art of healing, to give the patient at one time two different medicinal substance."