When "how much" is used together with verbs, such as in this case (how much does he EAT), कितना is always used. Neither कितने nor कितनी is used in those cases.

If however "how much" is used with a noun, all three variations (कितना, कितने and कितनी) can be used, depending on the object.

Examples are:

"how many bananas does he eat" = वह कितने केले खाता है

"how many books" = कितनी किताबें

"how tall is she" = वह कितनी लंबी है

"how tall is he" = वह कितना लंबा है