To get an even number the unit digit should be 0,2, 4 or 6 and hundred digit can't be 0.

If unit digit is 2, hundred digit can be 1,3,4,5 or 6 (5 possibilities) and tens digit can be 0 or any of the 4 digits remaining after filling hundreds place(5 possibilities). By fundamental principle of counting, no. of 3 digit numbers that can be formed=5*5=25.

Similarly, when units digit 4 (or 6), we get 25 numbers.

Now if units digit is 0, hundred digit can be 1,2,3,4,5,6 (6 possibilities) and tens digit can be any of the remaining 5 digits. So, no.of 3 digit numbers=5*6=30.

Hence, total no .of 3-digit numbers=25+25+25+30=105