How could you use 5 times 6 equals 30 to find the product of 6 times 6?

By itself you cannot. However, you can use the distributive property of multiplication over addition as follows:

6*6 = (5+1)*6 = 5*6 + 1*6

Now, you are told that 5*6 = 30 and if you do not know that 1*6 = 6 you are in trouble!

So the above sum is 30+6 = 36.