This is a 2 part question. The first part of which I have
calculated..."An equilibrium mixture holds 1.5 moles H2(g), 8.00 moles
CO2(g), 1.00 mole H20(g) and 3.00 moles CO(g) in a 5.00 liter
container, what is Kc for this mixture?" With the balanced equation I
determined that Kc = .25. The second part of the question, a
continuation of the first part, I do not know how to complete..."How
many moles of H2 (gas) must be added to the container in order to
increase the amount of CO to 3.50 moles?"

I know this has something to do with stoichiometry but I'm not sure
how to approach this and get the correct answer. Help would be greatly
appreciated.

This looks like a homework problem so I won't give you the answer but
I will tell you how to set it up.

You already have the equation and you have the correct value for the
equilibrium constant, Kc. Let 'x' be the number of moles of hydrogen
that you have to add, so the total amount of hydrogen initially will
be (1.5 + x) moles, but this will decrease as the system reaches a new
equilibrium. The number of moles of CO2 will also decrease and the CO
and water will increase. The CO has to increase from 3 to 3.5 moles.
Because of the stoichiometry, the number of moles of H2O must increase
by the same amount and the CO2 and H2 have to decrease by that same
amount. With this information, you should be able to set up an
equation with 'x' as the only unknown. Solve for 'x' and you've got
your answer.