Sure....
Explanation:
As x & y are the co-prime.

Case 01: x = 1 and y = 1.
Here, 2(x) = 2, and 3(y) = 3
So, the greatest common divisor(GCD)=1

Case 02: x = 1 and y = 2.
Here, 2x = 2, and 3y = 6
So, the GCD=2

Case 03: x = 3 and y = 2.
Here, 2x = 6, and 3y = 6
So, the GCD=6

Case 04: x = 3 and y = 4.
Here, 2x = 6, and 3y = 12
So, the GCD=6

That means GCD is different with different value of x & y.

So the Answer is not fixed; that means "Can not be determined: E"

Let's test some pairs of values....

case i: x = 1 and y = 1 have a greatest common divisor of 1
Here, 2x = 2(1) = 2, and 3y = 3(1) = 3
So, the greatest common divisor of 2x (2) and 3y (3) is 1

case ii: x = 1 and y = 2 have a greatest common divisor of 1
Here, 2x = 2(1) = 2, and 3y = 3(2) = 6
So, the greatest common divisor of 2x (2) and 3y (6) is 2

Answer: E

You can play around with giving y a 3 or x a 2 in order to get different combinations of shared factors for 2x and 3y, so we don't know:

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