x = first integer
x+2 = second integer just after the first, and it is even
x+4 = third even integer
x+6 = fourth even integer
Add up the four integers and set that result equal to -52. Then solve for x
(x)+(x+2)+(x+4)+(x+6) = -52
x+x+2+x+4+x+6 = -52
4x+12 = -52
4x+12-12 = -52-12
4x = -64
4x/4 = -64/4
x = -16
So the first integer is -16
The second integer is x+2 = -16+2 = -14
The third integer is x+4 = -16+4 = -12
and the fourth integer is x+6 = -16+6 = -10
So in summary the four consecutive even integers are -16, -14, -12, and -10
Note how they add to -52:
(-16)+(-14)+(-12)+(-10) = -52