$P = \sqrt{11 - 4\sqrt{7}} - \dfrac{2}{\sqrt{7} + 3} - \sqrt{28}$

$P = \sqrt{7 - 4\sqrt{7} + 4} - \dfrac{2(3 - \sqrt{7})}{(3 + \sqrt{7})(3 - \sqrt{7})} - \sqrt{4 \cdot 7}$

$P = \sqrt{(\sqrt{7} - 2)^2} - \dfrac{2(3 - \sqrt{7})}{3^2 - (\sqrt{7})^2} - 2\sqrt{7}$

$P = |\sqrt{7} - 2| - \dfrac{2(3 - \sqrt{7})}{2} - 2\sqrt{7}$

$P = \sqrt{7} - 2 - (3 - \sqrt{7}) - 2\sqrt{7}$ (do $\sqrt{7} > 2$)

$P = \sqrt{7} - 2 - 3 + \sqrt{7} - 2\sqrt{7}$

$P = (\sqrt{7} + \sqrt{7} - 2\sqrt{7}) - 2 - 3$

$P = -5$

Vậy $P = -5$.