Apoundal is the force required to accelerate a mass of 1 lbm at a rate of 1 ft/s2, and a slug is the mass of an object that will accelerate at a rate of 1 ft/s2 when subjected to a force of 1 lbf.
(
a. calculate the mass is slugs and the weight in poundals of a 175 lbm man (i) on earth and (ii) on the moon, where the acceleration of gravity is one-sixth of its value on earth.
(
b. a force of 355 poundals is exerted on a 25.0-slug object. at what rate (m/s2) does the object accelerate?

Remember the formula as per the second Law of Newton: F = m*a

And also remember that the weight is the force with which the mass is attracted by the planet (or satellite in the case of the moon).

With that information you can answer the questions:

a) Weight = F = m*a

m = 175 slugs = 175 lbm

i) Earth

a = 32.17 ft/s^2

Weight on Earth = 175 lbm * 32.17 ft / s^2 = 5,629.75 poundal

ii) Moon

a = [1/6] 32.17 ft/s^2

Weight on the Moon = [1/6]*5,629.75 poundal = 938.29 poundal

b) Force = 355 poundal
m = 25.0 slug

a in m/s^2 = ?

First calculate the force in ft/s^2

F = m*a => a = F/m = 355 poundal / 25.0 slug = 14.2 ft/s^2

Conversion:

14.2 ft / s^2 * [ 0.3048 m/ft] = 4.32816 m/s^2

4.33 m/s^2

D-no effect on the rate