Sure, I can help with that! Let's solve the equation step-by-step:
Given equation:
[tex]\[ 2(3y - 4) = 3\left(y - \frac{2}{3}\right) \][/tex]
Step 1: Distribute the numbers on both sides.
On the left side:
[tex]\[ 2 \cdot 3y = 6y \][/tex]
[tex]\[ 2 \cdot (-4) = -8 \][/tex]
So, the left side becomes:
[tex]\[ 6y - 8 \][/tex]
On the right side:
[tex]\[ 3 \cdot y = 3y \][/tex]
[tex]\[ 3 \cdot \left(-\frac{2}{3}\right) = -2 \][/tex]
So, the right side becomes:
[tex]\[ 3y - 2 \][/tex]
We now have:
[tex]\[ 6y - 8 = 3y - 2 \][/tex]
Step 2: Move all terms containing [tex]\(y\)[/tex] to one side of the equation and constant terms to the other side.
Subtract [tex]\(3y\)[/tex] from both sides:
[tex]\[ 6y - 3y - 8 = 3y - 3y - 2 \][/tex]
[tex]\[ 3y - 8 = -2 \][/tex]
Step 3: Add 8 to both sides to isolate the term with [tex]\(y\)[/tex]:
[tex]\[ 3y - 8 + 8 = -2 + 8 \][/tex]
[tex]\[ 3y = 6 \][/tex]
Step 4: Divide both sides by 3 to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{6}{3} \][/tex]
[tex]\[ y = 2 \][/tex]
So, the solution is [tex]\( y = 2 \)[/tex].
Thus, the solution is [tex]\(\boxed{2}\)[/tex].
