How many atoms can hydrogen bond with carbon?
I think that the question is not clear enough. Can you be more specific?
If your question was something like this: how many atoms of hydrogen can be around carbon, then the answer is 4. Carbon forms 4 bonds with other atoms.
Please note that carbon need not always form bonds to four atoms. A carbon could form a double bond with an oxygen and then two single bonds to hydrogen atoms. The carbon is only bonded to three atoms, but is forming a total of four bonds (1 double and 2 singles).