How many times does the graph of 4x=32-x^2 cross the x axis

The number of times a graph crosses the x axis is the same as asking how many zeroes has the function represented by that graph.

The number of zeroes is given by the power of the independent variable, in this case x.

Given that the maximum power of x is 2, then the function has 2 zeroes and the graph crosses the x axis 2 times

the line crosses the x axis twice