Not much to do here other than to compute each of these.

\[\begin{align*}\left( {f \circ g} \right)\left( x \right) & = f\left[ {g\left( x \right)} \right] = f\left[ {\sqrt {6 + 7x} } \right] = 4\sqrt {6 + 7x} - 1\\ & \\ \left( {g \circ f} \right)\left( x \right) & = g\left[ {f\left( x \right)} \right] = g\left[ {4x - 1} \right] = \sqrt {6 + 7\left( {4x - 1} \right)} = \sqrt {28x - 1} \end{align*}\]