What is "the quotient of eight raised to the power of two and four, decreased by six."

Okay, let's try to break this down:

The quotient of 8 raised to the power of two and four, so that sounds like

x = (8^2)^4
Then decreased by 6

x = (8^2)^4 - 6

Let the quotient be x

Now then, we can start simplifying by exponents first:
(8^2)^4 = 8^8 = 16,777,216

Now subtract 6
16, 777, 216 - 6 = 16,777,210

So our quotient would be:
16,777,210!
:D