[tex]f(x)=\dfrac{1}{6}x+12\to y=\dfrac{1}{6}x+12[/tex]
Change x to y, and y to x.
[tex]x=\dfrac{1}{6}y+12[/tex]
solve for y:
[tex]\dfrac{1}{6}y+12=x\ \ \ |-12\\\\\dfrac{1}{6}y=x-12\ \ \ \ |\cdot6\\\\y=6x-72[/tex]
Your answer is:
[tex]f^{-1}(x)=6x-72[/tex]
