Let's denote Kelly's regular pay per hour as \( x \).
When she works overtime, she makes $10 more per hour. Therefore, her overtime pay per hour is \( x + 10 \).
She worked 8 regular hours and 4 overtime hours. The equation for her total earnings is:
\[ 8x + 4(x + 10) = 160 \]
Expanding the equation gives:
\[ 8x + 4x + 40 = 160 \]
Combining like terms:
\[ 12x + 40 = 160 \]
Next, we subtract 40 from both sides:
\[ 12x = 120 \]
Now, divide both sides by 12:
\[ x = 10 \]
So, Kelly's regular pay per hour is \($10\).
Therefore, the answer is:
\[ \boxed{10 \text{ per hour}} \]