Bài giải:

P + $\left( {{x}^{2}}-2{{y}^{2}}+\frac{2}{3}xy \right)=-4{{x}^{2}}+5{{y}^{2}}+\frac{2}{3}xy$

P = $\left( -4{{x}^{2}}+5{{y}^{2}}+\frac{2}{3}xy \right)-\left( {{x}^{2}}-2{{y}^{2}}+\frac{2}{3}xy \right)$

P = $-4{{x}^{2}}+5{{y}^{2}}+\frac{2}{3}xy-{{x}^{2}}+2{{y}^{2}}-\frac{2}{3}xy$

P = $(-4{{x}^{2}}-{{x}^{2}})+(5{{y}^{2}}+2{{y}^{2}})+\left( \frac{2}{3}xy-\frac{2}{3}xy \right)$

P = $-5{{x}^{2}}+7{{y}^{2}}$

Vậy đáp án đúng là: A