I'll give another example, maybe this will help. Cyclopentadiene also dimerizes when left sitting out, and the mechanism is a Diels-Alder reaction: https://lh5.googleusercontent.com/89doymsdl_ojvmKmvF4863ihLBzxWnMmV18I8c2qkhbA6r6sAk5wzZr8XI-ekZHbRse5qLkTi16f4tarpKlndquFD_I6bFam_UThxWPmsna0r8_F5XUTUXCko1GW00hqdVM
And correspondingly, here's the reverse, cracking it back into the monomers:
https://lh3.googleusercontent.com/d9spJz9wzBIfWL_q2xQlKLbvryATTav0aBc9C7HWrUQp94WNCGOOi8jT4rcN3IHKH4DbUZXCvzd4yAE6eFPHZtusgL9Ibf0kp0dfAqDI-SX5DrZkMOlB5ITII8ryh9v0_eA
So the dimer is really two of the original monomers fused together! By looking at the dimer in this example, we can see that the molecular formula is \(C_{10}H_{12}\) so the monomer, since it's exactly two stuck together, must be \(C_5H_6\), since I am just dividing by 2.
To start taking the first step in "cracking" this problem (terrible pun sadly intended) determine the molecular formula of this lactone (almost an epoxide, but slightly different!), and then divide all the subscripts by 2 to determine the molecular formula of the monomer! That's it!
After you do that, then this will at least allow you to try to create some possibilities blindly of what the original monomer might be, so if you can figure out all possible structures for the monomer (which might be surprisingly more challenging than you think) try to do that too and see what you get!