1. **State the problem:** Solve the equation $$6 \cdot \frac{| -12g |}{2} + 24 = 48$$ for $g$. 2. **Understand the absolute value:** The absolute value $| -12g |$ is equal to $12|g|$ because absolute value removes the negative sign. 3. **Rewrite the equation:** Substitute $| -12g |$ with $12|g|$: $$6 \cdot \frac{12|g|}{2} + 24 = 48$$ 4. **Simplify the fraction:** $$6 \cdot \cancel{\frac{12|g|}{2}}^{6|g|} + 24 = 48$$ 5. **Multiply:** $$6 \times 6|g| + 24 = 48$$ $$36|g| + 24 = 48$$ 6. **Isolate the absolute value term:** $$36|g| = 48 - 24$$ $$36|g| = 24$$ 7. **Divide both sides by 36:** $$\frac{36|g|}{\cancel{36}} = \frac{24}{\cancel{36}}$$ $$|g| = \frac{24}{36}$$ 8. **Simplify the fraction:** $$|g| = \frac{2}{3}$$ 9. **Solve for $g$:** Since $|g| = \frac{2}{3}$, $g$ can be either positive or negative: $$g = \frac{2}{3} \quad \text{or} \quad g = -\frac{2}{3}$$ **Final answer:** $$g = \pm \frac{2}{3}$$