The number of different 6-digit numbers that can be formed using the three digits 0,1 and 2 is

in the six places of the digits, the first place can be filled only by $0$1 or $2$ (if $0$ comes in first place, that makes it $5$ digit number) and the remaining places can be filled by any one of the $3$ digits.
So, first place has only $2$ choices and the remaining $5$ places have $3$ choices each.
Hence,the number of different $6$-digit numbers that can be formed using the three digits $0,1$ and $2$ = $2\times 3^5$