#### Answer

$k=\frac{3}{2}$, $y=\frac{3}{2}x$

#### Work Step by Step

If y varies directly as x, we know that the variables x and y can be related by the function $y=kx$, where k is the constant of proportionality.
If $y=6$ when $x=4$, then we know that $6=4k$. Divide both sides by 4.
$k=\frac{6}{4}=\frac{3}{2}$
Therefore, the constant of variation is $k=\frac{3}{2}$ and the direct variation equation is $y=\frac{3}{2}x$.