Why can't I seem to understand how to balance chemical equations?

I don't understand at all how to balance chemical equations. I need to pass my CHM100 class this summer to get my dental hygiene diploma. I am taking my CHM class online and am not doing well. What I don't understand about balancing chemical equations is where the coefficients come from? Our test is... show more I don't understand at all how to balance chemical equations. I need to pass my CHM100 class this summer to get my dental hygiene diploma. I am taking my CHM class online and am not doing well. What I don't understand about balancing chemical equations is where the coefficients come from? Our test is going to be formatted like so:

___Al +___O2-----> ___ Al2O3 and I do not get how it is balanced as

4 Al + 3 O2 -----> 2 Al2O3

Where does the 4, 3, and 2 come from???

We're also going to have to write and balance chemical equations for reactions, like:

Iron metal and sulfur powder are heated in the flask producing solid iron (II) sulfide
which is Fe + S ---> FeS

I don't understand why there are no subscripts or coefficients?

Any help would be much appreciated!
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