1. **State the problem:** We are given the circumference of a circle as $4\pi$ inches and need to find its radius $r$ in inches. 2. **Formula used:** The circumference $C$ of a circle is related to its radius $r$ by the formula: $$C = 2\pi r$$ 3. **Substitute the given circumference:** $$4\pi = 2\pi r$$ 4. **Solve for $r$:** Divide both sides by $2\pi$: $$\frac{4\pi}{\cancel{2\pi}} = \frac{2\pi r}{\cancel{2\pi}}$$ This simplifies to: $$2 = r$$ 5. **Answer:** The radius of the circle is $2$ inches.