first take the derivative of the function which is

4x+3, the derivative function tells you the slope at any point of the original function. you plug -2 into the derivative function to find the slope at the point. The slope is -5 . after that you us y=mx+b(where m is the slope) form to solve for your tangent line. you then plug in your slope and your given point (-2,6) into the question and solve for b. so you will end up with 6=-5(-2)+b when you solve for b you get -4. so your tangent line equation is y=-5x -4