In a ∆ABC, if a = 8, b = 9 and 3 cos C = 2,

a = 8 , b = 9

3 cosC = 2

$\Rightarrow \cos C=\frac{2}{3}$

also using, cosine formula 

$\cos C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}$

$\Rightarrow \frac{2}{3}=\frac{8^{2}+9^{2}-c^{2}}{2 \times 8 \times 9}$

$\Rightarrow 4 \times 8 \times 3=8^{2}+9^{2}-c^{2}$

$\Rightarrow C^{2}=8^{2}+9^{2}-12 \times 8$

= 49

i. e $C=7$