1. **State the problem:** Solve for $x$ in the equation $$\frac{96}{4x} + 11 = 14$$. 2. **Isolate the fraction:** Subtract 11 from both sides to get $$\frac{96}{4x} = 14 - 11$$. 3. Simplify the right side: $$\frac{96}{4x} = 3$$. 4. **Rewrite the equation:** $$\frac{96}{4x} = 3$$. 5. Multiply both sides by $4x$ to eliminate the denominator: $$\cancel{4x} \times \frac{96}{\cancel{4x}} = 3 \times 4x$$ which simplifies to $$96 = 12x$$. 6. **Solve for $x$:** Divide both sides by 12: $$\frac{96}{\cancel{12}} = \frac{12x}{\cancel{12}}$$ which simplifies to $$8 = x$$. 7. **Final answer:** $$x = 8$$.