なにで たべますか？ / By what do you eat?

で

this is a method marker.

なにで

なに means "what". なにで means "by what".

なにで　たべますか？

"たべますか? / eat?". So, this means "By what do you eat?". This is used when you want to ask which the person eat by chopsticks, spoon, fork or etc...

はしで　たべます。

Answering to the above question with "I eat by chopsticks.". "はし / chopsticks.".