How many photons are produced in a laser pulse of 0.175 J at 425 nm

For a single photon, E=hc/λ. For multiple photons, the energy increases proportionally.

first you have to find the energy of a single photon
h = 6.62 x 10^-34; c = 3 x 10^8

E=hc/(425 x 10^-9) = 4.67 x 10^-19 joules / photon

and since you have 0.175 joules of laser pulse

0.175 / (4.67 x 10^-19) = 3.74 x 10^17 photons