"Peter will eat in the evening."
Translation:पीटर शाम को खायेगा।
खायेगा is the masculine singular third-person form which you use when talking about someone else other than yourself and the listener. खाऊँगा is the masculine first-person form which you use when talking about yourself.
Eg: पीटर तरबूज खायेगा और मैं आम खाऊँगा - Peter will eat watermelon and I'll eat a mango