Answer
The coefficient of $x$ is $-6$ and the coefficient of $y$ is $3$.
Work Step by Step
Let the coefficient of $x$ be $A$ and $y$ be $B$.
The equation becomes
$Ax+By-12=0$ (I)
To calculate the $x\ \operatorname{intercept}$, substitute $y=0$ in the equation (I); that is,
$\begin{align}
& Ax+B\times 0-12=0 \\
& Ax-12=0 \\
& Ax=12 \\
& x=\frac{12}{A}
\end{align}$
It is given that the $x\ \text{intercept}=-2$.
$\begin{align}
& -2=\frac{12}{A} \\
& -2A=12 \\
& A=\frac{12}{-2} \\
& =-6
\end{align}$
Now,
To calculate the $y\ \text{intercept}$, substitute $x=0$ in equation (I); that is,
$\begin{align}
& A\times 0+By-12=0 \\
& By-12=0 \\
& By=12 \\
& y=\frac{12}{B}
\end{align}$
It is provided that the $y\ \text{intercept}=4$.
$\begin{align}
& 4=\frac{12}{B} \\
& B=\frac{12}{4} \\
& =3
\end{align}$
Hence, the coefficient of $x$ is $-$ 6 and the coefficient of $y$ is 3.
