$3x-6 \geq \frac{ x+6 }{ 3 }$
Multiply both sides of the inequality by $3$$9x-18 \geq x+6$
Move the variable to the left-hand side and change its sign$9x-18-x \geq 6$
Move the constant to the right-hand side and change its sign$9x-x \geq 6+18$
Collect like terms$8x \geq 6+18$
Add the numbers$8x \geq 24$
Divide both sides of the inequality by $8$$\begin{align*}&x \geq 3 \\&\begin{array} { l }x \in \left[ 3, +\infty\right\rangle\end{array}\end{align*}$