$P=\dfrac{6^{2016}+4}{6^{2016}}\\ P=\dfrac{6^{2016}+4}{6^{2016}}\\ =\dfrac{6^{2016}}{6^{2016}}+\dfrac{4}{6^{2016}}\\ =1+\dfrac{4}{6^{2016}}\\ <1+\dfrac{4}{6^{2016}-4}\\ =\dfrac{6^{2016}-4}{6^{2016}-4}+\dfrac{4}{6^{2016}-4}\\ =\dfrac{6^{2016}-4+4}{6^{2016}-4}\\ =\dfrac{6^{2016}}{6^{2016}-4}\\ <\dfrac{6^{2016}}{6^{2016}-5}\\ =Q$
Vậy $P<Q$