Consider that the intercept form of the equation of a line whose x-intercept is 'a' and y-intercept is 'b', is given by,
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]The given equation of the line is,
[tex]6x-3y=24[/tex]Transpose the terms to convert the equation in intercept form,
[tex]\begin{gathered} \frac{1}{24}\cdot(6x-3y)=1 \\ \frac{6x}{24}-\frac{3y}{24}=1 \\ \frac{6x}{6\cdot4}-\frac{3y}{3\cdot8}=1 \\ \frac{x}{4}-\frac{y}{8}=1 \\ \frac{x}{4}+\frac{y}{(-8)}=1 \end{gathered}[/tex]Comparing with the standard form,
[tex]\begin{gathered} a=4 \\ b=-8 \end{gathered}[/tex]Thus, the x-intercept and y-intercept of the line, respectively, are
[tex]4,-8[/tex]