Quantity B: \(4^2 \sqrt{2^2} = 16 * 2 = 32\)

Quantity A: \(2^2 \sqrt{x} = 4\sqrt{x}\)

If x < 64, then Quantity A will be less than Quantity B.
I.e., if x = 16, Quantity A is 16.

If x > 64, then Quantity A will be greater than Quantity B.
I.e., if x = 81, Quantity A is 36.

Therefore, the relationship cannot be determined from the given info.