Question

check whether 6n can end with the digit 0 for any natural number n

Answer 1

no because it's prime factor is 2*3
but number end with digit zero has its prime factor 2*5
but it doesn't have 5 as it's prime factor
so it doesn't end with digit zero.

Answer 2

ANSWER

Yes. 

Let the value of $n$ be $5$. 
$n=5$
Then, 
$6n=6*5=30$

The number 30 ends with the digit 0. 

Hope this may help you.