Binomial Theorem - Coefficients in Products of Binomial Expansions

Given that the coefficient of \({{x}^{2}}\) in the expansion of \({{\left( 1+2x \right)}^{4}}{{\left( 1-px \right)}^{5}}\) is \(1674\), find the possible values of the constant \(p\).

Hence, find the possible coefficients of \({{x}^{2}}\) in the expansion of \({{\left( 1+2x \right)}^{4}}{{\left( 1+\frac{px}{2} \right)}^{5}}\).