We are given a matrix equation $[2p \quad 3]\begin{bmatrix} 4 \\ -6 \end{bmatrix} = [6]$ and need to find the value of $p$.

1. Problem Description

We are given a matrix equation $[2p \quad 3]\begin{bmatrix} 4 \\ -6 \end{bmatrix} = [6]$ and need to find the value of $p$.

2. Solution Steps

First, perform the matrix multiplication:

$[2p \quad 3]\begin{bmatrix} 4 \\ -6 \end{bmatrix} = (2p)(4) + (3)(-6) = 8p - 18$.

Now, we can set this result equal to 6:

$8p - 18 = 6$.

Next, add 18 to both sides of the equation:

$8p = 6 + 18$

$8p = 24$.

Finally, divide both sides by 8 to solve for $p$:

$p = \frac{24}{8}$

$p = 3$.

3. Final Answer

The value of $p$ is 3.