An object weighs 59N on earth where g is 9.8N/kg. Find the acceleration due to gravity on a planet where the same object weighs 40.5N

Use Newton's second law.

The object's mass is the same everywhere, so first compute the mass using the object's weight on Earth:

F = ma   ⇒   59 N = m (9.8 N/kg)   ⇒   m ≈ 6.02041 kg

Now compute the acceleration on the other planet:

F = ma   ⇒   40.5 N ≈ (6.02041 kg) a

⇒   a ≈ 6.72712 m/s² ≈ 6.7 m/s² ≈ 1.5g

where g = 9.8 m/s², just to express this acceleration relative to the gravitational acceleration at Earth's surface.