The molecular formula C4H6 represents a hydrocarbon with 4 carbon atoms and 6 hydrogen atoms. To determine the total number of cyclic isomers possible for this hydrocarbon, we need to consider the different ways in which the carbon atoms can be arranged to form cyclic structures.

Determining the number of cyclic isomers can be done by analyzing the different possibilities for the carbon skeleton and the presence of double bonds. Let's break down the analysis into two key factors: the carbon skeleton and the presence of double bonds.

1. Carbon skeleton:
The carbon atoms can be arranged in different ways to form cyclic structures. We can have:

- A chain of 4 carbon atoms connected in a straight line, forming a butane molecule.
- A chain of 3 carbon atoms with one carbon atom branching off, forming an isobutene molecule.
- A chain of 2 carbon atoms with two carbon atoms branching off, forming a 2-methylpropene molecule.

2. Presence of double bonds:
In addition to the carbon skeleton, we need to consider the presence of double bonds. The hydrocarbon C4H6 has the molecular formula suggesting the presence of one double bond. This double bond can be located in different positions within the carbon skeleton.

Considering all the possibilities mentioned above, we can have the following cyclic isomers:

- Cyclobutene: A cyclic structure with a double bond between two adjacent carbon atoms.
- Methylcyclopropene: A cyclic structure with a double bond between a carbon atom in the ring and a carbon atom branching off.
- 1,3-Butadiene: A cyclic structure with a double bond between two non-adjacent carbon atoms.
- Cyclobutane: A cyclic structure without any double bonds.

Therefore, the total number of cyclic isomers possible for a hydrocarbon with the molecular formula C4H6 is 4.

In summary, by considering the different possibilities for the carbon skeleton and the presence of double bonds, we can determine that there are 4 different cyclic isomers possible for a hydrocarbon with the molecular formula C4H6.