Four such integers are 8, -7, -9, and -10
(8)(-7)(-9)(-10) = -5040 which is less than 0
and
(8)+(-7)+(-9)+(-10) = -18
There are many possibilities:
Four other such integers are 1, -4, -7, and -8
(1)(-4)(-7)(-8) = -224 which is less than 0
and
(1)+(-4)+(-7)+(-8) = -18
Edwin