Aaaand, the explanation...
First off, a league is a unit of measure equal to about five and a half kilometers. It is completely irrelevant what unit of measure you use for the riddle other than to help foil any attempts to merely google the answer. The solution, in any case, is that the man's front door is situated precisely upon the north pole, so that despite walking east, he remains the same distance from his porch. The surface of the earth, being a spherical plane, demonstrates the rules of elliptic geometry quite well. As the riddle is completely hypothetical, one may disregard the fact that there is no house on the North pole, unless you still believe in Santa.
It seems that a new conundrum is in order-- and another math joke. Attempting to remember to post one did not seem to be very effective in making me post more often... I'm out of good, relevant riddles, so we'll have a paradox this time. Curry's paradox, to be precise. And I'm too lazy to actually write it out, so here's an image that explains it pretty well:
Math joke: Why do mathematicians always confuse Halloween and Christmas?
Answer: Because Oct 31 = Dec 25
Explanation: "Oct" means octal, which is base 8, and "Dec" is decimal, base 10, which is what we normally use for numbers. In base 8, 25 is written as 31.
First conundrum source
Second conundrum was mentioned in Euclid's Window (Mlodinow), image from here.