A2kg object weighs 19.6n on earth. if the acceleration due to gravity on mars is 3.71 meters per second what is the object mass on earth

The acceleration due to gravity at the Earth's surface is 9.8 m/s/s 

So a 2 kg object will accelerate at 9.8 m/s/s if it is dropped actually all dropped objects will accelerate at the same rate. 

The force of gravity on the object is given by Newton's 2nd Law 

F = m . a 

F = 2 . 9.8 = 19.6 N 

Now go to Mars , with a lower gravitational field strength. It only accelerates falling objects at 3.71 m/s/s 

So the force of gravity on the object is F = 2 . 3.71 = 7.42 N 

But the answer is (2) 2 kg, because the mass of the object stays the same and that is what you are asked for. 
Someone was trying to be tricky.