If a and b are distinct positive integers. the units digit of a2 is equal to the units digit of a, and the units digit of b2 is equal to the units digit of
b. if the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b?

The units digit of a squared number is equal to the units digit of that number only for digits 1 (1^2=1), 5 (5^2=25) and 6 (6^2=36). So a and b must end with 1, 5 or 6.

Now let's try all the combinations of these:

1*5=5, not good since 5 is already used.
1*6=6, not good since 6 is already used.
5*6 =30, unit digit 0, not used!!

so a*b has units digit 0.

The answer is poppy pants69