1. **State the problem:** Solve for the unknown denominator $x$ in the equation $$4 \div \frac{23}{x} = \frac{20}{23}.$$\n\n2. **Recall the division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$4 \div \frac{23}{x} = 4 \times \frac{x}{23}.$$\n\n3. **Rewrite the equation:** $$4 \times \frac{x}{23} = \frac{20}{23}.$$\n\n4. **Multiply both sides by 23 to clear the denominator:** $$4x = 20.$$\n\n5. **Solve for $x$ by dividing both sides by 4:** $$x = \frac{20}{4} = 5.$$\n\n6. **Final answer:** The unknown denominator is $5$.