Given the equation
[tex]4=-\frac{2}{3}x[/tex]The objective is to solve for x, this means that the x terms must remain alone in one side of the equation. The x term is being multiplied by -2/3, to cancel this multipication you have to divide it by -2/3, and, to keep the equality valid any operation performed in one side of the equation must be performed in the other side of the equation, so you have to divide 4 by -2/3 too:
[tex]\begin{gathered} 4=-\frac{2}{3}x \\ \frac{4}{-\frac{2}{3}}=\frac{-\frac{2}{3}}{-\frac{2}{3}}x \\ 4\cdot(-\frac{3}{2})=(-\frac{2}{3})(-\frac{3}{2})x \\ -6=x \end{gathered}[/tex]