\(f(x)=\frac{x^2-6}{4x-8}
\\
\\f(8)=\frac{8^2-6}{4\times8-8}= \frac{58}{24} = \frac{29}{12}
\\
\\f(6)=\frac{6^2-6}{4\times6-8}= \frac{30}{16} = \frac{15}{8}
\\
\\ \frac{f(8)-f(6)}{8-6} =\frac{\frac{29}{12} - \frac{15}{8} }{2} =\frac{\frac{116}{48} - \frac{90}{48} }{2} =\frac{\frac{26}{48} }{2} =\frac{26}{96}=\frac{13}{48}\)