1. The problem is to find the value of $x$ in the equation $$\frac{3x+2}{5} = 4.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$. The key rule is to perform the same operation on both sides of the equation to maintain equality.\n\n3. Multiply both sides of the equation by 5 to eliminate the denominator:\n$$5 \times \frac{3x+2}{5} = 5 \times 4$$\nThis simplifies to:\n$$\cancel{5} \times \frac{3x+2}{\cancel{5}} = 20$$\n$$3x + 2 = 20$$\n\n4. Subtract 2 from both sides to isolate the term with $x$:\n$$3x + 2 - 2 = 20 - 2$$\n$$3x = 18$$\n\n5. Divide both sides by 3 to solve for $x$:\n$$\frac{3x}{3} = \frac{18}{3}$$\n$$\cancel{3}x / \cancel{3} = 6$$\n$$x = 6$$\n\n6. The solution is $x = 6$. This means when $x$ is 6, the original equation holds true.