Number of cyclic isomers of C4H6
You can answer such questions using D.U. (Degree of unsaturation)

The formula is $\mathrm{C + 1 - }\frac{H + X - N}{2}$

C = Carbon.
H = Hydrogen.
X = Halogen.
N = Nitrogen.


If you get D.U. to be one, then in the structure there could be:


1 double bond.
1 ring.


Let's take an example of $\ce{C4H8}$ which has D.U. equal to one.


It can have three structures of 1 double bond:





It can have two structures of 1 ring:




Now for D.U. equal to two, the possibilities are:


2 double bond.
2 ring.
1 double bond and 1 ring.
1 triple bond.


Let's take your example of $\ce{C4H6}$ which has D.U. equal to two:


It can have two structures of 2 double bond:





It can have one structure of 2 ring:





It can have four structures of 1 double bond + 1 ring:





It can have two structures of 1 triple bond:




So, the answer is 5 cyclic isomers as you can see above.