Answer :
Let's begin by identifying key information given to us:
[tex]\begin{gathered} \frac{13}{14}-\frac{6}{7}x=\frac{7}{8} \\ \text{Rearranging the expression, we have:} \\ \frac{13}{14}-\frac{7}{8}=\frac{6}{7}x \\ \frac{52-49}{56}=\frac{6}{7}x \\ \frac{3}{56}=\frac{6}{7}x \\ \text{Cross multiply to eliminate the denominators, we have:} \\ 7\times3=6\times56\times x \\ 21=336x\Rightarrow336x=21 \\ 336x=21 \\ x=\frac{21}{336}=\frac{1}{16} \\ x=\frac{1}{16} \\ \\ \therefore x=\frac{1}{16} \end{gathered}[/tex]