This phrase expresses a very strong sense of impossiblity. The verb is usually in the potential form.
tigert
「たくさんあって、とても食べきれません」 fits with the translation if you read it carefully...
nicemon
Ex#6603...the potential form of 食べる Is 食べられる。。。So..the example must be...たくさんあって、とても食べられません。
gahoangdai
The example is correct. 食べきれません is in potential form. 食べ : masu form of "to eat" 切る : Used as an auxiliary verb to mean "to finish an action completely" 切る became 切れる and then 切れません