$$\frac{\sqrt{84}}{2}}\times\sqrt3\\\\
=\frac{\sqrt{4\times 21}}{2}\times\sqrt3\\\\
=\frac{\sqrt{4}\times \sqrt{21}}{2}\times\sqrt3\\\\
=\frac{2\times \sqrt{21}}{2}\times\sqrt3\\\\
=\sqrt{21}\times\sqrt3\\\\
=\sqrt{7}\times\sqrt3 \sqrt3\\\\
=3\sqrt{7}\\\\$$
.