#### Answer

$y=-30$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use $
y=kx
$ and solve for the value of $k$ with the given $x$ and $y$ values. Then use the equation of variation to solve for the value of the unknown variable.
$\bf{\text{Solution Details:}}$
Since $y$ varies directly as $x$, then $y=kx.$ Substituting the given values, $
y=20
$ and $
x=4
,$ then the value of $k$ is
\begin{array}{l}\require{cancel}
20=k(4)
\\\\
\dfrac{20}{4}=k
\\\\
k=5
.\end{array}
Hence, the equation of variation is given by
\begin{array}{l}\require{cancel}
y=kx
\\\\
y=5x
.\end{array}
If $x=-6,$ then
\begin{array}{l}\require{cancel}
y=5x
\\\\
y=5(-6)
\\\\
y=-30
.\end{array}