$fog(x)=6x-8 \\ g(x)=2x-3 \\ f(g(x))=6x-8 \\ f(2x-3)=6x-8 \\ 2x-3 \to x \\ x \to \frac{x+3}2 \\ f(x)=6\frac{x+3}2-8=3x+9-8=3x+1$