Can you please tell me which one is correct:

Either by X or by Y or Either by X or Y

Are both acceptable? Thanks.

GK,

As either of those constructions is grammatically acceptable, your question concerns stylistic preference more than correctness.

For example, Next week I plan to travel for Thanksgiving either by train or plane is grammatically correct, as is Next week I plan to travel for Thanksgiving either by train or by plane.

Hope that helps.
-dan

Thanks a lot Dan. That is very helpful.

Also, is the same true for:
'by either x or y' & 'by either x or by y'?

I don't think "either by plane or train" is considered parallel in general - and especially not on the GMAT. In the construction "either X or Y," the 'X' part (which here is by plane) and the 'Y' part (which here is train) have to be EXACTLY parallel - which means that both of them should contain prepositions.

For instance:
1. Next year we'll go either to Calgary or Edmonton: Wrong
2. Next year we'll go either to Calgary or to Edmonton: Right
3. Next year we'll go to either Calgary or Edmonton: Right
4. Next year we'll go to either Calgary or to Edmonton: Wrong
In each of these cases, figure out what is the 'X' and what is the 'Y' in the either X or Y construction, and verify for yourself that the construction really is parallel.

There are some words that can be omitted from parallel constructions - for instance, see #40 in the purple Verbal guide: 'elected to retire early rather than face', which eliminates the 'to' from the second infinitive. However, I've NEVER seen a GMAT problem omit a preposition in a parallel construction, so it seems that parallel prepositions are sacrosanct (and can't be 'understood' like the to in the above infinitives).

I just looked through all the sentence correction problems in both OGs, and I didn't see a single example of a sentence eliminating a preposition in a parallel construction. So it's probably a safe bet that you should never do so.

Finally, to answer your most recent question, 'by either x or y' is analogous to #3 above and so is correct; 'by either x or by y' is analogous to #4 and is thus incorrect. In any case, DON'T memorize these forms - there are just way too many of them. Instead, just find what's 'X' and what's 'Y', ignore all the other words (hard to do, but learn to do it), and look for exact parallelism.

HTH.