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You will choose one fish first, will not replace it, and will choose a second fish.
There are 18 + 22 = 40 fish in the tank.
There are 18 goldfish at first.
The probability the first fish taken out is a gold fish is 
p(first fish is goldfish) = 18/40 = 9/20

Now you will take the second fish. After taking the first goldfish, there are 39 fish left. There are 17 goldfish left.
The probability the second fish is a goldfish is 
p(second fish is goldfish) = 17/39

To find the probability of both fish being goldfish, multiply the probabilities together.
p(taking two goldfish) = 9/20 * 17/39 = 153/780 = 51/260

Option C. 51/260