1.Lucy looks like her mother.
= Lucy looks the same as her mother.
= Lucy and her mother look alike.
2.I think it is a big box.
= I think it (to be) a big box.
3.I like collecting stamps best.
= I enjoy/love collecting stamps best/most.
= My favorite hobby is collecting stamps.
= Collecting stamps is my favorite hobby.
4.At/On Christmas,they got a lot of presents.
= They got/received lots of presents at/on Christmas.
= They got/received many presents at/on Christmas.