B is correct. "afraid to" is normally used of things you can choose to do or not do: "I was afraid to ask", "I was afraid to walk into the room". "afraid of" is normally used of things you have no choice about or control over: "I was afraid of falling", "I was afraid of the fierce dog".
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gravediggerA. The bath was icy, so I walked very carefully. I was afraid to fall.I say "I am afraid to..." when I mean that I would not voluntarily do something because of some fear.
gravediggerThe path was icy. I was afraid to walk.I was afraid to walk on the path because it was icy and I could get no traction, so I walked on the