Hi
Please see below. If I am not mistaken, the red answer is incorrect because it does not answer how but answers where.
A- “How are you going?”
B- “[color=red]I am going walking.” VERSUS “[color=blue]I am going on foot.”
A- “Where are you going?”
B- “[color=blue]I am going walking.”
Tom
Hi Tom
A couple of comments. 
A- “How are you going?”
B- “[color=red]I am going walking.” => [color=red]You’re right. This is wrong.
VERSUS
“[color=blue]I am going on foot.” => [color=blue]It would be more natural to simply say “On foot.”
A- “Where are you going?”
B- “[color=blue]I am going walking.” => [color=blue]A more natural answer would be “For a walk.”
Amy