how do you solve the quadratic inequality x^2+x-12<4x

The left-hand side is an upward curving quadratic and the right-hand side is a straight line with a positive slope that cuts through the quadratic at two points.  To see this draw curves of y = x²+x-12 and y = 4x on the same graph

Treat it as an equality first and find the two values of x that solve the equality, then the values of x in between those two give the range in which the inequality holds.