Answer :
Let us assume that the first even number is x
Then the first consecutive even is x + 2
The second consecutive even is x + 4
The third consecutive even is x + 6
The four consecutive even numbers are
x, x + 2, x + 4, x + 6
Their sum is -252, then
Add them and equate the sum by -252
[tex]x+x+2+x+4+x+6=-252[/tex]Add the like terms on the left side
[tex]\begin{gathered} (x+x+x+x)+(2+4+6)=-252 \\ 4x+12=-252 \end{gathered}[/tex]Now let us solve the equation
Subtract 12 from both sides
[tex]\begin{gathered} 4x+12-12=-252-12 \\ 4x=-264 \end{gathered}[/tex]Divide both sides by 4 to find x
[tex]\begin{gathered} \frac{4x}{4}=\frac{-264}{4} \\ x=-66 \end{gathered}[/tex]That means, the first even number is -66
-66 + 2 = -64
-66 + 4 = -62
-66 + 6 = -60
The four consecutive even numbers are
-66, -64, -62, -60
Let us find their sum to check the answer
-66 + -64 + -62 + -60 = -252
Then the answer is right
The greatest integer is -60