Answer
x-intercept = 7
y-intercept = -6
Refer to the image below for the graph.
Work Step by Step
Write the equation in $Ax +By=C$ form.
This will make solving for the intercepts a lot easier.
The given equation can be rewritten as:
$6x-7y-42=0
\\6x-7y-42+42=0+42
\\6x-7y=42$
To find the $x$ intercept, set $y=0$ then solve for $x$ to obtain:
$6x-7y=42
\\6x-7(0) = 42
\\6x=42
\\\dfrac{6x}{6}=\dfrac{42}{6}
\\x=7$
The x-intercept is $7$.
To find the $y$ intercept, set $x=0$ then solve for $y$ to obtain:
$6x-7y=42
\\6(0)-7y = 42
\\-7y=42
\\\dfrac{-7y}{-7}=\dfrac{42}{-7}
\\y=-6$
The y-intercept is $-6$.
To draw the graph of the equation, plot the x-intercept point $(7, 0)$ and the y-intercept point $(0, -6)$ and connect them using a straight line.
(refer to the attached image in the answer part above)