The number of three-digit even numbers, formed by the digits 0, 1,...

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 $= 20 + 16 + 16 = 52$