$$\frac{\frac{4x}{x}+\frac{2}{x}}{\frac{x}{3}+\frac{1}{6}}$$
Since $\frac{4x}{x}$ and $\frac{2}{x}$ have the same denominator, add them by adding their numerators.$$\frac{\frac{4x+2}{x}}{\frac{x}{3}+\frac{1}{6}}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $6$ is $6$. Multiply $\frac{x}{3}$ times $\frac{2}{2}$.$$\frac{\frac{4x+2}{x}}{\frac{2x}{6}+\frac{1}{6}}$$
Since $\frac{2x}{6}$ and $\frac{1}{6}$ have the same denominator, add them by adding their numerators.$$\frac{\frac{4x+2}{x}}{\frac{2x+1}{6}}$$
Divide $\frac{4x+2}{x}$ by $\frac{2x+1}{6}$ by multiplying $\frac{4x+2}{x}$ by the reciprocal of $\frac{2x+1}{6}$.$$\frac{\left(4x+2\right)\times 6}{x\left(2x+1\right)}$$
Factor the expressions that are not already factored.$$\frac{2\times 6\left(2x+1\right)}{x\left(2x+1\right)}$$
Cancel out $2x+1$ in both numerator and denominator.$$\frac{2\times 6}{x}$$
Expand the expression.$$\frac{12}{x}$$