**Solution: **

If the number 6^{n} ends with the digit zero (0), then it should be divisible by 5, as we know any number with the unit’s place as 0 or 5 is divisible by 5.

Prime factorization of 6^{n} = (2 × 3)^{n}

Therefore, the prime factorization of 6^{n} doesn’t contain the prime number 5.

Thus, it is clear that for any natural number n, 6^{n }is not divisible by 5.

Hence, it proves that 6^{n} cannot end with the digit 0 for any natural number n.