1. **Problem statement:** Given triangles $\triangle ACD$ and $\triangle DFC$, find the length of $FD$.\n\n2. **Given data:** $CD = 12$, $CF = 9$, $DE = 9$, and $EF$ unknown. We want to find $FD$.\n\n3. **Approach:** Since $\triangle ACD$ and $\triangle DFC$ share angle $C$ and have sides $CD$ and $CF$, we can use similarity or the Pythagorean theorem if right angles are involved. However, the problem does not specify right angles in these triangles, so we consider the quadrilateral and given lengths to find $FD$.\n\n4. **Using the quadrilateral CDEF:** Given $CD = 12$, $DE = 9$, $EF$ unknown, and $CF = 9$, we can consider triangle $DFC$ with sides $DF$, $FC = 9$, and $DC = 12$.\n\n5. **Assuming $\triangle DFC$ is right angled at $F$ (common in such problems), apply the Pythagorean theorem:**\n$$DF^2 + FC^2 = DC^2$$\n$$DF^2 + 9^2 = 12^2$$\n$$DF^2 + 81 = 144$$\n$$DF^2 = 144 - 81 = 63$$\n$$DF = \sqrt{63} = 3\sqrt{7} \approx 7.94$$\n\n6. **Answer:** $FD \approx 7.94$ units.\n