1. **State the problem:** Solve the equation $ (x - 2)(x - 1) = 6 $ for $x$. 2. **Use the distributive property (FOIL) to expand the left side:** $$ (x - 2)(x - 1) = x^2 - x - 2x + 2 = x^2 - 3x + 2 $$ 3. **Rewrite the equation:** $$ x^2 - 3x + 2 = 6 $$ 4. **Bring all terms to one side to set the equation to zero:** $$ x^2 - 3x + 2 - 6 = 0 $$ $$ x^2 - 3x - 4 = 0 $$ 5. **Factor the quadratic equation:** We look for two numbers that multiply to $-4$ and add to $-3$. These are $-4$ and $1$. $$ x^2 - 3x - 4 = (x - 4)(x + 1) = 0 $$ 6. **Set each factor equal to zero and solve for $x$:** $$ x - 4 = 0 \Rightarrow x = 4 $$ $$ x + 1 = 0 \Rightarrow x = -1 $$ 7. **Solution set:** $$ \boxed{\{4, -1\}} $$ These are the values of $x$ that satisfy the original equation.