$v\hat i = \left( {6\hat i + 8\hat J} \right)\,m/s$

$u = \sqrt {u_x^2 + u_y^2} $$ = \sqrt {{6^2} + {8^2}} = 10 \,m/s$

$\tan \theta = \frac{{{u_y}}}{{{u_x}}} = \frac{8}{6}$$ = \frac{4}{3}$

$\therefore \,\sin \theta = \frac{4}{5}$and $\cos \theta = \frac{3}{5}$

$R = \frac{{{u^2}\sin 2\theta }}{g}$

$ = \frac{{{u^2}2\sin \theta \cos \theta }}{g}$

$ = \frac{{{{(10)}^2} \times \,2 \times \,\frac{4}{5} \times \,\frac{3}{5}}}{{10}}$

$R = 9.6\,meter$