How do you solve -10x - 6 < - 4x 12

You have a typo

-10x - 6 < - 4x 12
might mean
-10x - 6 < - 4x + 12 ???
if so
-10 x < - 4 x + 12
-6 x < 12 now divide by -6, change arrow direction because negative
x > -2
===================
check
x = 0 should satisfy
-10x - 6 < - 4x + 12
-6 < +12 sure enough