How many four-digit numbers can be formed using the digits $0,1,2,3, 4,5$ without repetition?

 For a four-digit number, we have to fill four places and $0$ cannot appear in the first place (thousand's place).

For the first place, there are five choices ($0,1,2,3, 4,5$); Second place can then be filled in five ways ( $0$ and remaining four-digits); Third place can be filled in four ways (remaining four-digits); Fourth place can be filled in three ways (remaining three-digits).

Total number of ways =$5\times 5\times 4\times 3=300$

$\Rightarrow 300$ four-digits numbers can be formed.