Problem: Solve the equation $x/2 - 6 = 8 - 2x/3$. 1. Move terms to combine like terms. Add $\frac{2x}{3}$ to both sides and add 6 to both sides to isolate variable terms on the left and constants on the right. This gives the equation $$\frac{x}{2}+\frac{2x}{3}=14$$ 2. Combine the fractions on the left. Find a common denominator and add: $$\frac{x}{2}+\frac{2x}{3}=\frac{3x}{6}+\frac{4x}{6}=\frac{7x}{6}$$ So we have $$\frac{7x}{6}=14$$ 3. Solve for $x$. Multiply both sides by $\frac{6}{7}$ to get $$x=14\cdot\frac{6}{7}$$ Simplify the multiplication: $$x=2\cdot6=12$$ 4. Check the solution by substitution. Left side: $\frac{12}{2}-6=6-6=0$. Right side: $8-\frac{2\cdot12}{3}=8-\frac{24}{3}=8-8=0$. Both sides equal 0, so $x=12$ is the correct solution. Final answer: $x=12$.