Make x the subject of, 4(x+1)/(x+2) = y

The fundamental rule to keep in the back of your head is 'whatever happens to one side must happen to the other'. This way we can be sure that whatever is on the left hand side of the equals sign will be the same as whatever is on the right hand side.
Then follow these 5 steps: (1) Multiply all terms by the bottoms of any fractions. (2) Expand any brackets. (3) Move any terms with the letter we interested in over to one side. Put all the other terms on the other side. (4) Factorise out the letter we are interested in. (5) Divide both sides by the resulting factor.
(1): 4(x+1) = y(x+2) (2): 4x+4 = yx+2y (3): 4x-yx = 2y-4 (4): x(4-y) = 2y-4 (5): x = (2y-4)/(4-y)