To solve the equation by multiplying both sides by 2, we will start with:
\[ \frac{2}{3}(4 + 3b) = 2 + 2b \]
Multiply both sides by 2:
\[ 2 \cdot \frac{2}{3}(4 + 3b) = 2 \cdot (2 + 2b) \]
This simplifies to:
\[ \frac{4}{3}(4 + 3b) = 4 + 4b \]
Now, to get rid of the fraction, we multiply both sides by 3. The equation then becomes:
\[ 4(4 + 3b) = 3(4 + 4b) \]
Now, let's expand both sides:
\[ 16 + 12b = 12 + 12b \]
Next, we'll isolate the variable. We can subtract \(12b\) from both sides:
\[ 16 = 12 \]
This is an inconsistency, which implies that there is no solution to the original equation since we derived a contradiction.
Thus, the final result of the left side simplifies out as demonstrated, but there is no solution when fully solved—indicating the two sides are unequal.