Saline solution and dose of drugs? Chemistry help.?

50kg x (2mg / kg?hr) x (1g / 1000mg) x (1L / 5g) = 0.02 L / hr

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any idea what I'm doing here?

look at the units...
kg x (mg / kg?hr) ---> mg/hr

then...
mg/hr x (g / mg) ----> g/hr

then...
g / hr x (L/g) ---> L/hr

this is an interesting UNIT conversion PROBLEM.  Set the problem up solving for Volume(V) and set it equal to the mass of the person 50kg.  Then select the conversion factor that will cancel kg.

V/hr = 50 kg x (2 mg/kg/hr)  = 100 mg/hr  NOTICE that hr is in the required denominator position stated in the question.

 This will give units in mg/hr.  Since mg is not a volume unit, select a conv. factor that will cancel mg.  There is none. So find a mass unit given in the problem.  It is 5g per liter. This means you should then convert mg to grams before going any further. (Obtain this conv. factor from the metric conversion charts in your text or from memory)

V/hr = 100 mg / hr x ( 1 g / 1000 mg) =  0.1 g / hr  

 NOTICE that mg cancels out leaving gram unit as given in the question.  You are not yet at the required unit of volume per hr. so next choose the conv. factor in the question that will contain gram AND volume.  It is 5 g/L. so one more step is needed.

V/hr = 0.1 g / hr x (1 L / 5 g) = 0.02 L / hr .  NOTICE that the g unit is needed in the denominator so it can cancel out the g in the remainder shown above. ANY given factor can be inverted as needed to cancel an unwanted unit. The problem answer now has the required units.Since the problem does not specify WHICH volume unit you should have, you have solve the question as asked.
HOWEVER, most likely another conversion should be used to produce the answer in mL units since 0.02 L is an awkward value. If that is the case, simply find the conv. factor between L and mL and apply it as was done above.