如果问''你能帮我搬这箱子吗?''答:Would you like a hand to carry this box?不对吧?

应为Would you like to bear me a hand to carry this box?

bear a hand
v.
出一把力, 帮助, 参与, 插一手

我也觉得不是很对。你这样写好像变成“我可以帮你搬这个箱子吗？”应该是Would you like to give me a hand to carry this box?
我自己的这句话也不知道对不对，不过楼上的几句不错。

Can you give me a hand with the box?
Can you help me to carry the box ?