let the 3 consecutive integers be 2x-2, 2x, 2x+2 where x is integer

the sum of the three consecutive even integers is -243

2x - 2 + 2x + 2x + 2 = -243

6x = -243

x = -243/6

x = 40.5 is not integer thus there are no such consecutive even integers.

Second way of solving this problem: the sum of even integers (in our case 3 even integers) is even integer and -243 is not even thus there are no such even integers.