Question

iwould you like to do sth和would you like sth to是等同的吗，如Would you like something to drink

What about 后面是跟动词+ing吗

Answer 1

举例说明：
would you like to do sth: 你想要做...事,委婉询问对方，或征求对方意见.
意思无大的变化，主要在成分不一样.
例：
Would you like water to drink?
你需要一些喝的水？（意在强调这个水是能喝的），也就是drink是water的定语.（喝的）

Would you like to drink water?
你需要喝水吗？（不对水做强调）这里的drink 是谓语.
What about ：about 是介词，介词后面只能跟名词，代词，动名词等，你说的动词+ing也就是动名词，是没错的。
如：
what about starting a company from scratch?

若有不明，请追问

Answer 2

Q：i would you like to do sth和would you like sth to是等同的吗
A：不等同~
i would you like to do sth 是我想要你做某事
would you like sth to 则是你想要。。。？
前者是请求要求，后者是询问商量~

Q：What about 后面是跟动词+ing吗
A：有这么用的~ 但是多数情况下用 How about
比如：How about going on a trip with us?
What about 一般接名词~
比如：what about him?

Answer 3

前者是想要做某事，后者to do 是sth的后置定语 What about 后面是跟动词+ing