The answer to the question "Such a wooden box __that is heavy ___" is the first one" like; to lift". This is because you cannot use "as" to connect with the immediate word "that". Also, the use of "to be lifted" would be inappropriate in the sentence.
None of the available choices are correct. Having the word "such" at the beginning makes either the "like" or "as" completely redundant, so you can't really use any of those answers and be confident that you've chosen the correct one. That's my opinion anyway, I'd refuse to choose any of them, flip my desk over and storm out in a rage.