Step 1 :Distribute -6 to both 4 and \(\frac{2}{3}\), which gives us \((-6)(4)+(-6)\left(\frac{2}{3}\right)\).
Step 2 :Calculate \((-6)(4) = -24\) and \((-6)\left(\frac{2}{3}\right) = -4\).
Step 3 :Add the results: \(-24 - 4 = -28\).
Step 4 :Therefore, \(-6\left(4 \frac{2}{3}\right) = -28\).
Step 5 :So, the final answer is \(\boxed{-28}\).