Question

show that 6n cannot end with the digit 0 for any natural number

Answer 1

 6 = 2 x 3
  6n = (2 x 3) n
     3 never ends with 0
 therefore 6 never ends with 0 

Answer 2

6 is obtained by 2x3.
therefore it is a multiple of 3.
Multiples of 3 never end with 0.

Therefore 6n where n is natural cannot end with 0.