SOLUTION
From the question, we can see that the sides of the diagram are similar.
Taking ratio of the similar sides we have
[tex]\begin{gathered} \frac{6}{8}=\frac{6+a}{8+4} \\ \end{gathered}[/tex]
Solving we have
[tex]\begin{gathered} \frac{6}{8}=\frac{6+a}{8+4} \\ \frac{6}{8}=\frac{6+a}{12} \\ cross\text{ multiplying we have } \\ 8\times\left(6+a\right)=6\times12 \\ 48+8a=72 \\ 8a=72-48 \\ 8a=24 \\ a=\frac{24}{8} \\ a=3 \end{gathered}[/tex]
Hence the answer is a = 3
