Time Taken by Pipe R Alone

In 2 hours, P, Q, R fill $\frac{2}{6} = \frac{1}{3}$ of the tank. Remaining work = $\frac{2}{3}$ filled by P and Q in 7 hours. So P and Q can fill full tank in $7 \times \frac{3}{2} = \frac{21}{2}$ hours. Rate of R = $\frac{1}{6} - \frac{2}{21} = \frac{7 - 4}{42} = \frac{3}{42} = \frac{1}{14}$. So R alone takes 14 hours.