Answer
$\begin{bmatrix} \frac{9}{2} &1\\-4&\frac{9}{4}\end{bmatrix} $
Work Step by Step
When we multiply a scalar $k$ with a matrix $A$, then the product will be the matrix $kA$, each of whose elements is $k$ times the corresponding element of $A$.
Our aim is to compute $\dfrac{3}{4}A-B$, so for this we will multiply each element of the matrix $A$ by $\frac{3}{4}$ and every element of $B$ by $-1$, then subtract them .
Therefore, we have:
\begin{align*}
\frac{3}{4}A-B&=\frac{3}{4} \begin{bmatrix} -2 &4\\0&3\end{bmatrix} - \begin{bmatrix} -6 &2\\4&0\end{bmatrix}\\ \\&=\begin{bmatrix} -\frac{3}{2} & 3\\0&\frac{9}{4}\end{bmatrix} -\begin{bmatrix} -6 &2\\4&0\end{bmatrix}\\ \\&=\begin{bmatrix} -\frac{3}{2}-(-6) \quad&3-2\\0-4\quad&\frac{9}{4}-0\end{bmatrix}\\
\\&=\begin{bmatrix} -\frac{3}{2}+6 \quad&1\\-4\quad&\frac{9}{4}\end{bmatrix}\\
\\&=\begin{bmatrix} \frac{9}{2} &1\\-4&\frac{9}{4}\end{bmatrix}
\end{align*}
