Answer
The formula was proved for $n=1$
The formula is correct if $n$ is changed by $n+1$
Work Step by Step
Let's prove the formula for $n=1$:
$n(n+1)=1(1+1)=1(2)=2$
It is correct!
Now, suppose that the formula is correct, that is:
$2+4+6+...+2n=n(n+1)$
Now, let's prove the formula for $n+1$:
$2+4+6+...+2n+2(n+1)=(2+4+6+...+2n)+2(n+1)=n(n+1)+2(n+1)=(n+2)(n+1)=(n+1)(n+2)=(n+1)[(n+1)+1]$
That is exactly the given formula if $n$ is changed by $n+1$
