Answer
The obtuse angle $B\approx 127{}^\circ $.
Work Step by Step
Consider the given expression $\cos B=\frac{{{6}^{2}}+{{4}^{2}}-{{9}^{2}}}{2\cdot 6\cdot 4}$.
$\begin{align}
& \cos B=\frac{{{6}^{2}}+{{4}^{2}}-{{9}^{2}}}{2\cdot 6\cdot 4} \\
& \cos B=\frac{36+16-81}{48} \\
& \cos B=-\frac{29}{48} \\
& B={{\cos }^{-1}}\left( \frac{-29}{48} \right)
\end{align}$
This implies $B\approx 127{}^\circ $.
