In this, I wrote x>-3 but the answer is x<-3. The direction seem to have flipped. But doesn’t the direction flips when we multiply or divide by negative value. Why did flip here, all we did was take the positive 3 other side. Can someone please clear this for me?

Correct.

The problem with what you did is that while x + 3 > 0 when x > -3, that isn’t the case for the x - 2 part. So you’ll be multiplying a positive and negative number, which is negative.