I don't understand why choosing "a" is right because they are not different: "denied" and "refused".
"He was seen stealing the bicycle but he ........doing that.
b. denied to steal
d. refused to steal
These words don't mean the same thing. "To deny" means "to claim something is false" "to refuse" means "to say you will not do something". Here he is saying "I did not steal the bike" "I deny stealing the bike". He cannot "refuse to steal the bike" (ie say "I will not steal this bike even if you try to force me to) because we know he already has stolen it.