Here, we have to determine the value of \(fg\left( {h\left( {2,5,7,3} \right),4,6,8} \right)\).
Given,
\(\begin{array}{l}
h\left( {p,q,r,s} \right) = remainder\;of\frac{{p \times q}}{{r \times s}}if\;\left( {p \times q} \right) > \left( {r \times s} \right)\\
\;\left( {or} \right)remainder\;of\frac{{r \times s}}{{p \times q}}\;if\;\left( {r \times s} \right) > \left( {p \times q} \right)
\end{array}\)
So, we obtain \(h\left( {2,5,7,3} \right) = remainder\;\left( {\frac{{7 \times 3}}{{2 \times 5}}} \right) = 1\)
Therefore, we get
\(fg\left( {h\left( {2,5,7,3} \right),4,6,8} \right) = fg\left( {1,4,6,8} \right)\)
Again, we have
\(\begin{array}{l}
f\left( {p,q,r,s} \right) = max\left( {p,q,r,s} \right)\\
g\left( {p,q,r,s} \right) = min\left( {p,q,r,s} \right)
\end{array}\)
So, we obtain
\(\begin{array}{l}
fg\left( {1,4,6,8} \right) = f\;\left( {1,4,6,8} \right) \times g\left( {1,4,6,8} \right)\\
= max\left( {1,4,6,8} \right) \times min\left( {1,4,6,8} \right)\\
= 8 \times 1\\
= 8
\end{array}\)
Hence, the value of desired function is
\(fg\left( {h\left( {2,5,7,3} \right),4,6,8} \right) = fg\left( {1,4,6,8} \right) = 8\)