Verified Answer :

\(7 \times 2 \frac{3}{7} \\ \\ 7 \times \frac{2 \times 7 + 3}{7} \\ \\ 7 \times \frac{14+3}{7} \\ \\ 7 \times \frac{17}{7} \\ \\ \frac{119}{7} \\ \\ 17 \\ \\ Answer: \fbox {17}\)

TSO

\(2 \frac{3}{7} = \frac{(2\cdot7)+3}{7} = \frac{14+3}{7} = \frac{17}{7}\)

\(7 \cdot \frac{17}{7} = \boxed{\bf{17}}\)