1. **Problem Statement:** Find the value of $x$ in the equation $$\frac{2x+4}{3} = 6.$$\n\n2. **Formula and Rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. This involves multiplying both sides by the denominator to eliminate the fraction, then simplifying and solving the resulting linear equation.\n\n3. **Step-by-step Solution:**\n\nMultiply both sides by 3 to cancel the denominator:\n$$\cancel{3} \times \frac{2x+4}{\cancel{3}} = 6 \times 3$$\nwhich simplifies to\n$$2x + 4 = 18.$$\n\n4. Subtract 4 from both sides to isolate the term with $x$:\n$$2x + 4 - 4 = 18 - 4$$\n$$2x = 14.$$\n\n5. Divide both sides by 2 to solve for $x$:\n$$\frac{\cancel{2}x}{\cancel{2}} = \frac{14}{2}$$\n$$x = 7.$$\n\n**Final answer:** $x = 7$