JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Permutations and Combinations

A three-digit even number formed from these digits needs a non-zero leading digit and a units digit drawn from $0,4,6$, so the two restrictions interact and the count splits by the units digit.
With units digit $0$, the leading digit may be any of the five remaining digits and the middle digit any of the four still left, giving $5\times 4=20$ numbers.
With units digit $4$ or $6$, the leading digit must avoid both $0$ and the chosen units digit, leaving $4$ choices, and the middle digit then has $4$ choices, giving $2\times 4\times 4=32$ numbers.
The number of such three digit even numbers is $20+32=52$.