1. **Problem:** Find the equation of the circle with center $(-1, 2)$ and diameter $6$. 2. **Formula:** The equation of a circle with center $(h, k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Important rule:** Diameter $d$ is twice the radius $r$, so: $$ r = \frac{d}{2} $$ 4. **Calculate radius:** Given diameter $d = 6$, radius is: $$ r = \frac{6}{2} = 3 $$ 5. **Substitute values:** Center $(h, k) = (-1, 2)$ and $r = 3$ into the circle equation: $$ (x - (-1))^2 + (y - 2)^2 = 3^2 $$ $$ (x + 1)^2 + (y - 2)^2 = 9 $$ 6. **Answer:** The equation of the circle is: $$ (x + 1)^2 + (y - 2)^2 = 9 $$ This corresponds to option (d).