First way: without using algebra (but your teacher won't
accept it!).

There are 3 of them so they must be right around 1/3 of -36, 
which is -12, so the integers are -12, 2 less and 2 more than -12, 
so the answer is -14, -12, and -10, and the smallest is -14.

Using algebra (which your teacher will accept):

n = smallest even integer
n+2 = middle-sized integer
n+4 = largest even integer

n + (n+2) + (n+4) = -36

Solve that for n.  You'll get -14

Edwin