Question

Check whether $6^{n}$ can end with the digit 0 for any natural number n

Answer 1

$6^n$ can never end with 0.

see
6¹ = 6
6² = 36
6³ = 216
6⁴ = 1296
whatever may be the value of n be, the unit digit is always 6. It will never be 0.