-4x<12.
Add 4x to each side: 0<12+4x, then subtract 12 from each side: -12<4x. Now divide each side by 4: -3<x.
This says that -3 is less than x, which is the same as saying, x is greater than -3, which we write as x>-3. So it’s not the inequality that’s reversed, but the quantities have swapped sides. x started off on the left side while 12 was on the right. In the process of solving for x, x ended up on the right side and 12 on the left. The pointy side of the inequality shows which quantity is the smaller. So in the original inequality, -4x is on the pointy side so it’s smaller than 12. The inequality doesn’t change. We ended up with -3 on the pointy side, and when the inequality was swapped round just to make it more readable and meaningful, the pointy side was still pointing to -3. When we swapped the inequality we also swapped where x and -3 were. It was just another way of writing the answer. We could just have left it as -3<x.