**Solution :**

If the number 6^{n} ends with the digit zero,then it is divisible by 5.Therefore the prime factorization of 6^{n }contains the prime 5.This is not possible because the only prime in the factorization of 6^{n} is 2 and 3 and the uniqueness of the fundamental theorem of arithmetic guarantees that these are no other prime in the factorization of 6^{n}

Hence, it is very clear that there is no value of n in natural number for which 6^{n} ends with the digit zero.