What are the intercepts of 7x-6y=8?

To find the x-intercept, let y = 0. Then $x = \frac{8}{7}$.
To find the y-intercept, let x = 0. Then $y = - \frac{8}{6} = - \frac{4}{3}$.
The equation of the linear function in standard form is $y = \frac{7}{6} x - \frac{4}{3}$ and the graph is shown below for verification of the intercept points.