Answer
Transform the equation.
$$X(s)=\frac{F(s)}{s^{2}+8 s+1}$$
Thus
$$F(s)-X(s)=F(s)-\frac{F(s)}{s^{2}+8 s+1}=\frac{s^{2}+8 s}{s^{2}+8 s+1} F(s)$$
Because $F(s)=6 / s^{2}$
$$F(s)-X(s)=\frac{s^{2}+8 s}{s^{2}+8 s+1} \frac{6}{s^{2}}=\frac{s+8}{s^{2}+8 s+1} \frac{6}{s}$$
From the final value theorem,
$$f_{s s}-x_{s s}=\lim _{s \rightarrow 0} s[F(s)-X(s)]=\lim _{s \rightarrow 0} s \frac{s+8}{s^{2}+8 s+1} \frac{6}{s}=8$$
Work Step by Step
Transform the equation.
$$X(s)=\frac{F(s)}{s^{2}+8 s+1}$$
Thus
$$F(s)-X(s)=F(s)-\frac{F(s)}{s^{2}+8 s+1}=\frac{s^{2}+8 s}{s^{2}+8 s+1} F(s)$$
Because $F(s)=6 / s^{2}$
$$F(s)-X(s)=\frac{s^{2}+8 s}{s^{2}+8 s+1} \frac{6}{s^{2}}=\frac{s+8}{s^{2}+8 s+1} \frac{6}{s}$$
From the final value theorem,
$$f_{s s}-x_{s s}=\lim _{s \rightarrow 0} s[F(s)-X(s)]=\lim _{s \rightarrow 0} s \frac{s+8}{s^{2}+8 s+1} \frac{6}{s}=8$$
