1. **State the problem:** Solve the equation $8(2x+3)-4=120$ for $x$. 2. **Apply the distributive property:** Multiply 8 by each term inside the parentheses. $$8(2x+3) = 8 \times 2x + 8 \times 3 = 16x + 24$$ So the equation becomes: $$16x + 24 - 4 = 120$$ 3. **Simplify the left side:** Combine like terms. $$16x + (24 - 4) = 16x + 20$$ So the equation is: $$16x + 20 = 120$$ 4. **Isolate the term with $x$:** Subtract 20 from both sides. $$16x + \cancel{20} - \cancel{20} = 120 - 20$$ $$16x = 100$$ 5. **Solve for $x$:** Divide both sides by 16. $$\frac{16x}{\cancel{16}} = \frac{100}{\cancel{16}}$$ $$x = \frac{100}{16}$$ 6. **Simplify the fraction:** $$x = \frac{25}{4}$$ **Final answer:** $$x = \frac{25}{4}$$