Explanation:
"I can walk that distance and have done so many times."

This means:

The speaker is able to walk the distance (can walk),

And they have done it repeatedly in the past (have done so many times).

The sentence implies familiarity and habitual action—the speaker is accustomed to doing it.

Now let's analyze the options:
A. I am used to walk that distance
— Incorrect grammar. It should be “used to walking,” not “used to walk.”
Incorrect

B. I used to walk that distance
— This means the speaker did it in the past but no longer does, which contradicts the original meaning.
Incorrect

C. I used to walking that distance
— Grammatically incorrect. “Used to” should be followed by a verb in base form or “be used to” + verb-ing.
Incorrect

D. I am used to walking that distance
— Correct. This means the speaker is accustomed to walking the distance, which matches the idea of having done so many times.
Correct

E. I will walk that distance
— This only talks about the future, and misses the idea of habit or repetition in the past.
Incorrect