Write the formulas of the compound Al+3 formed by specified cations with the following anions:OH-, NO3-, CO3-2,HSO4-, PO4-3 . Use the given order of anions

You should be learning to do this yourself.
Here is the easy way and one you can do in your head.
Al^3+ and NO3^-

In your mind write +3 above Al and write -1 above NO3. Place parentheses around the NO3. Mentally draw an X. The left leg goes from the 3 above Al to the bottom of the parentheses on NO3. Place the 3 at the bottom of that leg. The right leg goes from the -1 above (NO3) to the bottom of the l(ell) on Al. The number 1 goes there and you ignore the - sign.
Al1(NO3)3. You don't need to write a 1 so the formula is Al(NO3)3. All you are doing is transposing the valences of one cation/anion to the other.
Al and CO3 is Al2(CO3)3.
What about Mg and O.
That will give you Mg2O2 BUT always use the lowest numbers; write it as MgO. There are some compounds which don't follow this rule (Hg2Cl2, for example, and a few others) but you will learn those exceptions as you go along.