To solve the equation \( 12 + \frac{8}{x} = 16 \), follow these steps:

1. Subtract 12 from both sides of the equation to isolate the term with \( x \):
\[
\frac{8}{x} = 16 - 12
\]

2. Simplify the right side:
\[
\frac{8}{x} = 4
\]

3. To solve for \( x \), multiply both sides of the equation by \( x \) to get rid of the fraction:
\[
8 = 4x
\]

4. Divide both sides by 4 to isolate \( x \):
\[
x = \frac{8}{4}
\]

5. Simplify the right side:
\[
x = 2
\]

So, the solution to the equation \( 12 + \frac{8}{x} = 16 \) is \( x = 2 \).