First lets write down our starting conditions:
we have 22 gallons and it has 16% of ammonia
16% of 22 gallons is
A = 16/100*22 = 3,52 gallons
Now since only watter is evaporating that means that in second scenario after some watter evaporated there is still 3,52 gallons of ammonia. But now those 3,52 gallons of ammonia represent 24% of total mixture. So now we go other way.
24 % is 3,52 gallons
100% is x gallons
x = 100/24*3,52 = 14.667 gallons
That means that he has to evaporate
22 - 14.6667 = 7,333 gallons of water.
