so, we have the denominators of 3, 8, and 6, if we do a quick prime factoring on them, we can see that the LCD will be 24, so let's multiply both sides by the LCD to do away with the denominators.
[tex]\bf \cfrac{x-4}{3}+\cfrac{2x-3}{8}=\cfrac{5}{6}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{24}}{24\left(\cfrac{x-4}{3}+\cfrac{2x-3}{8} \right)=24\left( \cfrac{5}{6} \right)} \\\\\\ 8(x-4)+3(2x-3)=4(5)\implies 8x-32+6x-9=20 \\\\\\ 14x-41=20\implies 14x=61\implies x=\cfrac{61}{14}\implies x=4\frac{5}{14}[/tex]
