Line 1: [tex]$\quad \frac{3}{5} y - 8 = 4$[/tex]
Line 2: [tex]$\frac{5}{3} \cdot \frac{3}{5} y = 12 \cdot \frac{5}{3}$[/tex]
Line 3:
[tex]$\begin{array}{l}
y = \frac{60}{3} \\
y = 20
\end{array}$[/tex]

Penny's solving work is shown here. Has she solved this equation correctly?

A. Yes, Penny's work is correct and 20 is the correct solution.
B. No, Penny is wrong. She should have multiplied both sides by [tex]$\frac{5}{3}$[/tex].

Let's go through Penny's solution step-by-step to see if she solved the equation correctly:

1. Original Equation:
[tex]\[
\frac{3}{5}y - 8 = 4
\][/tex]
This is the equation Penny started with.

2. Step 1: Isolate the Term with [tex]$y$[/tex]:

To solve for [tex]$y$[/tex], first add 8 to both sides to move the constant term to the right side:
[tex]\[
\frac{3}{5}y - 8 + 8 = 4 + 8
\][/tex]
Simplifying this gives:
[tex]\[
\frac{3}{5}y = 12
\][/tex]

3. Step 2: Solve for [tex]$y$[/tex]:

Next, multiply both sides of the equation by the reciprocal of [tex]$\frac{3}{5}$[/tex], which is [tex]$\frac{5}{3}$[/tex]:
[tex]\[
\left(\frac{5}{3}\right) \cdot \frac{3}{5}y = 12 \cdot \frac{5}{3}
\][/tex]
This simplifies the left side to [tex]$y$[/tex] because [tex]$\frac{5}{3} \times \frac{3}{5} = 1$[/tex]:
[tex]\[
y = 12 \cdot \frac{5}{3}
\][/tex]

Now, calculate the right side:
[tex]\[
y = \frac{60}{3}
\][/tex]
Simplifying the division gives:
[tex]\[
y = 20
\][/tex]

4. Conclusion:

Yes, Penny correctly solved for [tex]$y$[/tex]. The solution [tex]$y = 20$[/tex] is indeed correct.