To find the number of real solutions for the equation \( u^2 = -64 \), we analyze the equation.
The left side, \( u^2 \), represents the square of a real number, which is always non-negative (i.e., \( u^2 \geq 0 \)). The right side of the equation is \(-64\), which is negative.
Since a non-negative number cannot equal a negative number, there are no real solutions to the equation \( u^2 = -64 \).
Thus, the answer is:
Zero real solutions.