Will you be at home at four o'clock?
Is correct this question?
I'm asking to another people if he will be in his house at that time.

"Will you be at home at four o'clock?"

Question

Will you be at home at four o'clock?
Is correct this question?
I'm asking to another people if he will be in his house at that time.

"Will you be at home at four o'clock?"

Answer

Yes, "Will you be at home at four o'clock?" is correct.

By the way, your other sentence should read:

I'm asking another person if he will be in his house at that time.

'Person' is the singular form of 'people', and we 'ask a person..' (not 'ask to..').

I hope that helps.