Chapter 6 - Section 6.6 - Rational Equations and Problem Solving - Exercise Set - Page 389: 62

$x=6$

By cross-multiplication and using the properties of equality, the solution to the given equation, $ \dfrac{x}{4}=\dfrac{x+3}{6} ,$ is \begin{array}{l} 6x=4(x+3) \\\\ 6x=4x+12 \\\\ 6x-4x=12 \\\\ 2x=12 \\\\ x=\dfrac{12}{2} \\\\ x=6 .\end{array}