To solve the problem, we first need to understand what it means for x to vary inversely with y. This means that the product of x and y is constant. Mathematically, we can express this as:

x * y = k

where k is a constant.

Initially, we know that x = 4 when y = 8. By substituting these values into our equation, we can find the value of k:

4 * 8 = k

k = 32

Now that we have the constant (k = 32), we can use this to find x when y = 16.

Substituting y = 16 into our inverse variation equation, we have:

x * 16 = 32

To isolate x, we divide both sides of the equation by 16:

x = 32 / 16

x = 2

Thus, when y equals 16, the value of x is 2.