Let's break down the problem given in the image.

The equation is:

$2 \begin{pmatrix} \frac{a}{3} & 2 \\ 1 & \end{pmatrix} + \begin{pmatrix} 4 & 0 \\ -1 & b \end{pmatrix} = \begin{pmatrix} 3 & \frac{2}{4} \\ \frac{2}{1} & \frac{d}{3} \end{pmatrix}$

To find the value of $a + b + c + d$, we need to solve for each variable by equating the elements on both sides of the matrices.

1. Solve for $a$:

$2 \cdot \frac{a}{3} + 4 = 3$ $\frac{2a}{3} + 4 = 3$ $\frac{2a}{3} = -1$ $a = -\frac{3}{2}$

2. Solve for $b$:

$2 \cdot 1 + b = \frac{d}{3}$

3. Solve for $c$:

$2 = \frac{2}{4}$

4. Solve for $d$:

$1 = \frac{d}{3}$ $d = 3$

Finally, calculate $a + b + c + d$. The possible options are given as:

• 13
• 15
• 17
• 19

Let's now compute.