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I think I managed to totally screw up my computer so I did already post this question, but from what I see it is gone now. I don't really know if its actually there or not cuz I can't do anything with computers but here is the question:

Hydrogen cyanide is produced industrially from the reaction of gaseous ammonia, oxygen, and methane.
2 NH3(g) + 3 O2(g) + 2 CH4(g) ¨ 2 HCN(g) + 6 H2O(g)
If 5.27x10^3 kg each of NH3, O2, and CH4 are reacted, what mass of H2O will be produced, assuming 100% yield?

You have the balanced equation:
first figure the amount of moles of ammonia, oxygen, and methane in the mass used. You need 1.5 times the methane amount of Oxygen.
So which is the limiting reactant? Just looking at it, I suspect it is O2, (working it in my head).

once I have the limiting reactant how do I go about calculating the mass of h20 produced? Dimensional Analysis would be a good way for me to understand it.

Sorry, I hit the wrong button.
Dimensional analysis will work. Just use the coefficients of the balanced equation.
For example,
mols starting material x (coefficient*product desired/coefficient*starting matrial) = mols product desired.