bridge question regarding answering opening of 1 of a major
I infer from the phrasing of your question that you are playing a 4-card Major  natural system such as Goren. If that is not the case please specify what system you are playing.

First, it is vital to correct your statement on the strength of the 1S response to 1H; it is not a limited strength bid of 6-9 HCP but an unlimited strength bid of 6-20+ HCP. It is absolutely forcing for one round on Opener, who is obligated to ensure that you get a second opportunity to call. While there are some unusual circumstances where an expert might make this call as a prepared bid with only 3 Spades, I would strongly recommend that you now forget I ever said that, and always treat it as showing 4 or more Spades.

Second, the principle of bidding 4-card suits up the line is a fundamental tenet of natural systems. Don't go bidding your best or strongest four card suit first; that will cause you to subsequently be lying about your overall hand shape. Bidding is a language and, just as in English, you cannot be scrambling the word order of your sentence and expect the meaning to be unchanged. "That is your cat." and "Is that your cat?" have different meanings in English, and reversing the order in which you show two suits also changes the meaning of your calls. When looking to see which denomination is the best to play in, total number of trumps is much more important than trump quality.

That being said, the 2H response to a 1S opening almost promises 5 Hearts; because, due to the above, it denies any other 4-card holding. It promises 10-20+ HCP, and either a 5-card Heart holding or a 3-4-3-3 hand shape for which either of a 1NT or 2S response was distasteful. With a flat 10 HCP I would prefer a 1NT or 2S response to bidding 2H with only 4, choosing between the two on whether my high cards were concentrated in one or two suits including spades or well distributed over at least three.  Update: In summary, when responding 2H over a 1S opening have either 5 Hearts or an extra point or two above the 10 HCP minimum.

Again - none of this applies unless you are playing a natural 4-card major system such as Goren. I suspect much of it applies to ACOL though never having played (or read much on) that system I am less familiar with it. In particular, if you are playing any of a 5-card Major system (whether Hardy or K-S style), a Forcing Club system, or Canape style responses none of the above will apply as written.