To add the fractions, we need to change each mixed fraction to improper fractions for ease of solving.
Hence:
[tex]\begin{gathered} 3\frac{7}{12}=\frac{(12\times3)+7}{12}=\frac{43}{12} \\ 2\frac{7}{9}=\frac{(9\times2)+7}{9}=\frac{25}{9} \end{gathered}[/tex]Next, we find the Lowest Common Multiples of the denominators (9 and 12)
[tex]L\mathrm{}C\mathrm{}M=36[/tex]Therefore, we can add as follows:
[tex]\begin{gathered} \frac{43}{12}+\frac{25}{9}=\frac{(3\times43)+(4\times25)}{36} \\ =\frac{129+100}{36} \\ =\frac{229}{36} \end{gathered}[/tex]To change back to mixed fraction:
[tex]\begin{gathered} \frac{229}{36}=6\frac{229-(6\times36)}{36} \\ =6\frac{13}{36} \end{gathered}[/tex]The answer is
[tex]6\frac{13}{36}[/tex]