Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

$\therefore$ The watch gains$ \left(2 + 4\dfrac{4}{5} \right) $min.or$ \dfrac{34}{5} $min. in 170 hrs.

Now,$ \dfrac{34}{5} $min. are gained in 170 hrs.

$\therefore$ 2 min. are gained in$ \left(170 \times\dfrac{5}{34} \times 2\right) $hrs= 50 hrs.

$\therefore$ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.