$EI ~ \theta_{AC} = 0$
$\frac{1}{2}(6)(3600) - 6M - \frac{1}{3}(3)(900) = 0$
$10\,800 - 6M - 900 = 0$
$M = 1650 \, \text{ lb}\cdot\text{ft}$ answer
$\delta_{max} = t_{A/C}$
$EI ~ \delta_{max} = EI ~ t_{A/C}$
$EI ~ \delta_{max} = (Area_{AC}) \cdot \bar X_A$
$EI ~ \delta_{max} = \frac{1}{2}(6)(3600)[ \, \frac{2}{3}(6) \, ] - 6M(3) - \frac{1}{3}(3)(900)[ \, 3 + \frac{3}{4}(3) \, ]$
$EI ~ \delta_{max} = 10\,800(4) - 18M - 900(5.25)$
$EI ~ \delta_{max} = 10\,800(4) - 18(1650) - 900(5.25)$
$EI ~ \delta_{max} = 8775 \, \text{ lb}\cdot\text{ft}^3$ answer