Hi,

I am uncertain about the proper placement of prepositions when using the words "either" or "both" For example, do you say:

We can meet either at your house or at the library.

OR

We can meet at either your house or the library.

Simply speaking, does the preposition come before either/both, or after it. I like the second one because I think it sounds better, but I don't know the rule.

Thanks in advance.

your examples are both fine.

in the constructions either X or Y and both X and Y, it's only important that the two parts labeled X and Y be grammatically parallel. whatever words come before 'either'/'both' don't count in the parallelism and can be ignored (although not, of course, ignored in the larger context of the passage).

therefore:
in the first example, X = 'at your house' and Y = 'at the library'. those are parallel (both are prepositional phrases).
in the second example, X = 'your house' and Y = 'the library'. those are parallel (both are location nouns).

you don't have to use prepositional phrases, of course:
you can choose EITHER to submit the paper incomplete but on time OR to submit the complete paper late and receive a penalty.
both parts are infinitives here, so the parallelism is good.