\(\displaystyle{6}{x}^{{2}}+{8}{x}+{4}\) and \(\displaystyle-{7}{x}^{{2}}-{7}{x}-{10}\)

Adding the given polynomial,

\(\displaystyle{\left({6}{x}^{{2}}+{8}{x}+{4}\right)}+{\left(-{7}{x}^{{2}}-{7}{x}-{10}\right)}\)

Removing the parentheses, we get

\(\displaystyle{\left({6}{x}^{{2}}+{8}{x}+{4}\right)}+{\left(-{7}{x}^{{2}}-{7}{x}-{10}\right)}={6}{x}^{{2}}+{8}{x}+{4}-{7}{x}^{{2}}-{7}{x}-{10}\)

Simplifying further by combining similar terms, we get

\(\displaystyle{6}{x}^{{2}}+{8}{x}+{4}-{7}{x}^{{2}}-{10}={6}{x}^{{2}}-{7}{x}^{{2}}+{8}{x}-{7}{x}+{4}-{10}\)

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

Hence, required answer is \(\displaystyle-{x}^{{2}}+{x}-{6}\)