What you want to do first is calculate what your original strength is per ml.
You have phenobarbital 20mg/5ml - if you divide 20mg by 5ml, that equals 4mg/ml
The formula for this problem is final volume over initial volume = initial strength over final strength.
Final volume is what you are solving for or (x)ml = 4mg is initial strength
Your initial volume is what you have on hand 100ml & 2mg is the final strength
Or (x)ml over 100ml = 4mg over 2mg; Then you cross multiply.
So that you would have 2mg times (x) = 100mg times 4mg or 2(x) = 400. Since you are solving for (x) you would divide 400 by 2 and you get 200ml. You already have 100ml so you would just need to add another 100ml of cherry syrup to your original 100ml to equal a concentration of 2mg/ml.
Hope that helps