\(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\14.5 \end{pmatrix}\),

\(\begin{pmatrix} 6 \times 2  + 4  \times m \\ 7 \times 2 + 5  \times m \end{pmatrix}\) = \(\begin{pmatrix} 24 \\ 29 \end{pmatrix}\),

12 + 4m = 24

4m = 24 - 12 = 12, then, m = 3 or 

14 + 5m = 29 

5m = 29 - 14 = 15, then, m = 3