In the reaction 2al2o3 ® 4al + 3o2, what is the mole ratio of aluminum to oxygen?

4:3 lol. Just so you know for future reference the numbers in front of the respective atoms/compounds usually represent the number of atoms to try and balance the equation. But in this context it is also a ratio and it is also the number of moles. An example would be this:

Mg+02 --> MgO - so one mole of Mg gives one mole of MgO. As you can see there are no numbers in front therefore it represents 1 mole.

Say you had 0.144 moles of Mg how many moles of MgO would be produced?

Using that concept (1 mol of Mg gives 1 mol of MgO)

0.144 mols would therefore be produced.

0.144 mol of Mg gives 0.144 mol of MgO.

If it was like your reaction it would go like this:

2moles of 2Al2O3 gives 4 moles of Al or 3 moles of 02

Anyway hope this helps it took me ages to get the hang of just that lol.