We have two inequalities that are linked with an "or", which means that so long as we have a valid #x# for one of the equations, it'll be part of the solution set (whereas if we had "and", we'd need the #x# values to be valid in both equations).
Let's solve them individually and see what we get:
Equation 1
#3(x-4)<12#
#x-4<4#
#x<8#
Equation 2
#4(x+3)<12#
#x+3<3#
#x<0#
Putting it together
We have #x<8# or #x<0#. Again, so long as we have a valid #x# value in one inequality, it's part of the solution.
#" OR "# means either of the conditions must be true.
#x<8#, since it includes all the solutions in #x<0# and more, is the final answer.
However, if it had been #x<0 " AND " x <8#, then BOTH conditions have to be true and the solution would be #x<0#