We have,

$0,1,3,4,6,7$

For three-digit even number, it must end with either $0, 4, 6$

The number of three -digit even numbers ending with $0$ is

$=5\times 4=20$

The number of three -digit even numbers ending with $4$

$=4\times 4=16$ 

The number of three -digit even numbers ending with $6$

$=4\times 4=16$

 Total three digits even numbers $=20+16+16=52$