1. **State the problem:** We are given two equations: $$8p - 9 = 6$$ and $$2p + 3q = 4$$ We need to find the value of $q$. 2. **Solve for $p$ from the first equation:** Add 9 to both sides: $$8p = 6 + 9$$ $$8p = 15$$ Divide both sides by 8: $$p = \frac{15}{8}$$ 3. **Substitute $p$ into the second equation:** $$2\left(\frac{15}{8}\right) + 3q = 4$$ Simplify: $$\frac{30}{8} + 3q = 4$$ $$\frac{15}{4} + 3q = 4$$ 4. **Isolate $3q$:** $$3q = 4 - \frac{15}{4}$$ Convert 4 to quarters: $$3q = \frac{16}{4} - \frac{15}{4} = \frac{1}{4}$$ 5. **Solve for $q$:** $$q = \frac{1}{4} \div 3 = \frac{1}{12}$$ **Final answer:** $$q = \frac{1}{12}$$