1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula for a circle's equation:** The standard form is $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $ (h, k) $ is the center and $ r $ is the radius. 3. **Identify the center and radius from the graph:** The center is approximately at $ (4, -2) $ and the radius is $ 2 $ units. 4. **Substitute the values into the formula:** $$ (x - 4)^2 + (y - (-2))^2 = 2^2 $$ 5. **Simplify the equation:** $$ (x - 4)^2 + (y + 2)^2 = 4 $$ 6. **Final answer:** The equation of the circle is $$ (x - 4)^2 + (y + 2)^2 = 4 $$ This equation represents a circle centered at $ (4, -2) $ with radius $ 2 $.