First, let's define the four consecutive even integers.

We can call the first even integer: #n#

The other 3 consecutive even integers will be by adding #2# to the previous integer (consecutive even integers are always 2 numbers apart).

So, the integers are:

#n#, #n + 2#, #n + 2 + 2 = n + 4# and #n + 4 + 2 = n + 6#

The sum of these four numbers equals #-28# or:

#n + (n + 2) + (n + 4) + (n + 6) = -28#

Solving for #n# gives:

#n + n + 2 + n + 4 + n + 6 = -28#

#n + n + n + n + 2 + 4 + 6 = -28#

#4n + 12 = -28#

#4n + 12 - color(red)(12) = -28 - color(red)(12#

#4n + 0 = -40#

#4n = -40#

#(4n)/color(red)(4) = -40/color(red)(4)#

#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -10#

#n = -10#

#n + 2 = -10 + 2 = -8#

#n + 4 = -10 + 4 = -6#

#n + 6 = -10 + 6 = -4#

The four consecutive even integers adding to -28 are:

#-10#, #-8#, #-6# and #-4#