Can you eat with chopsticks

The answer for the translation above is:
Hashi de taberu koto ga dekimasu ka?

I wrote: Tabemono o taberu de hashi koto ga dekimasu ka?
Would it be correct or just conceptually wrong?

~ koto ga dekiru is preceded by a verb. hashi is a noun. Therefore it'd be like saying "can you chopstick?" in English.

If you are asking that question of a non-Japanese (or someone from a non-chopstick culture), we'd usually say:
- Hashi o tsukaemasu ka? (Can you use chopsticks?) - if you know this conjugation.
or using the "- koto ga dekiru" construction:
- Hashi o tsukau koto ga dekimasu ka?

I wrote: Tabemono o taberu de hashi koto ga dekimasu ka?

As scarreddragon says, "- koto ga dekiru" needs to be preceded by a verb. So you need to string up:
- taberu koto ga dekimasu ka? (Can you eat?)
then you can add "with chopsticks":
- Hashi de taberu koto ga dekimasu ka? (Can you eat with chopsticks?)

You don't really have to add "tabemono o," as it is understood that what you eat with chopsticks is food.

Haha! I laughed way too hard at myself after realising my mistake, thanks guys! :)