(a) The composite function is,

\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}={f{{\left({g{{\left({x}\right)}}}\right)}}}\)

\(\displaystyle={f{{\left({x}-{2}\right)}}}\)

\(\displaystyle={4}{\left({x}-{2}\right)}^{{2}}-{6}\) [replacing x by x-2 in f(x)]

\(\displaystyle={4}{\left({x}^{{2}}-{4}{x}+{4}\right)}-{6}\)

\(\displaystyle={4}{x}^{{2}}-{16}{x}+{16}-{6}\)

\(\displaystyle{4}{x}^{{2}}-{16}{x}+{10}\)

b) Replacing x by -1 in the composite function, we get

\(\displaystyle{\left({f}\circ{g}\right)}{\left(-{1}\right)}={4}{\left(-{1}\right)}^{{2}}-{16}{\left(-{1}\right)}+{10}\)

=4+16+10

=30

\(\displaystyle{\left({f}\circ{g}\right)}{\left({x}\right)}={f{{\left({g{{\left({x}\right)}}}\right)}}}\)

\(\displaystyle={f{{\left({x}-{2}\right)}}}\)

\(\displaystyle={4}{\left({x}-{2}\right)}^{{2}}-{6}\) [replacing x by x-2 in f(x)]

\(\displaystyle={4}{\left({x}^{{2}}-{4}{x}+{4}\right)}-{6}\)

\(\displaystyle={4}{x}^{{2}}-{16}{x}+{16}-{6}\)

\(\displaystyle{4}{x}^{{2}}-{16}{x}+{10}\)

b) Replacing x by -1 in the composite function, we get

\(\displaystyle{\left({f}\circ{g}\right)}{\left(-{1}\right)}={4}{\left(-{1}\right)}^{{2}}-{16}{\left(-{1}\right)}+{10}\)

=4+16+10

=30