You will choose 1 cheese 3 different ways because there are three types of cheeses.
You will choose your topings 6 different ways. 4!/(2!2!) = 4*3/2 = 6
Therefore you will be able to get 6 * 3 different pizzas = 18 pizza combinations.
To confirm the toppings, suppose they are (M)ushrooms (P)epperoni (O)nions and (B)acon
M P
M O
M B
P O
P B
O B
Total 6.The order doesn't matter here. M O is the same thing as OM