How many grams of water (H2O) would you need to have the same number of molecules as 200 grams of ammonia (11.743 moles)?

Moles are molecule to molecule comparisons of the amounts of species.  So you have the moles of NH3 so then you only need to calculate the weight of the same number of moles of water:

11.743 moles X 18 g/mol = 211.37 g of H2O

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setup the solution with dimensional analysis

.. 200g NH3... . 1 mol NH3.. .  1 mol H2O... 18.02g H2O

 ---- ---- --- --- x ----- ----- ----- x ---- ---- ----- x ---- ---- ------ = __ g H2O

... .. . . 1.. .. .. ... 17.03g NH3.. 1 mol NH3.. .. 1 mol H2O

just enter

  200 / 17.03 * 18.02 = 

in your calculator