1. Problem statement: Create an equilibrium demand and supply diagram using linear functions $Q_d=24-4P$ and $Q_s=6+2P$. 2. Formula and rules: Market equilibrium occurs where demand equals supply, so set $Q_d=Q_s$. 3. Solve for the equilibrium price: $$24-4P=6+2P$$ Subtract 6 from both sides to isolate constant terms: $$24-4P-6=2P$$ Simplify the left side: $$18-4P=2P$$ Bring the $P$ terms together by adding $4P$ to both sides: $$18=6P$$ Divide both sides by 6 (showing cancellation of the divisor): $$\frac{18}{\cancel{6}}=\frac{6P}{\cancel{6}}$$ Therefore: $$3=P$$ 4. Find the equilibrium quantity by substituting $P=3$ into either equation: $$Q=24-4\cdot 3=24-12=12$$ Check with the supply function: $$Q=6+2\cdot 3=6+6=12$$ 5. Final answer and diagram notes: The equilibrium price is $P=3$ and the equilibrium quantity is $Q=12$. To sketch the diagram: plot price on the vertical axis and quantity on the horizontal axis. The demand line crosses the price axis at $P=6$ (point $(0,6)$) and the quantity axis at $Q=24$ (point $(24,0)$). The supply line crosses the price axis at $P=-3$ (point $(0,-3)$) and the quantity axis at $Q=6$ (point $(6,0)$). The intersection (equilibrium) is at $(12,3)$.