C and D are two points on the major arc AB of a circle with centre O…

Step 1. The equal angles. $C$ and $D$ lie in the same segment, so $\angle ACB = \angle ADB$.

Step 2. Solve. $3x + 6 = 5x - 18$ gives $24 = 2x$, so $x = 12$.

Step 3. The rim angle. $\angle ACB = 3 \times 12 + 6 = 42^\circ$.

Step 4. The centre. $\angle AOB = 2 \times 42^\circ = 84^\circ$.