I am working with Radarsat-2 quad-pol data and in many papers, I have come across the following processing step

“After filtering, the covariance matrix was converted to a symmetrized covariance matrix from which intensity backscatter (HH/HV/VV) and intensity ratios (HH/VV, HH/HV, HV/VV) were extracted.”

Can anyone tell me how to symmetrize the covariance matrix in SNAP?
The covariance matrix contains C11, C22,… elements. How is it possible to extract intensity backscatter from this matrix in SNAP?

You can derive the C-matrics from the S-matrix but not vice versa. Backscatter intensity is what you start with and you can formulate matrix representations [S, C, T] from it.

Symmetry in this context is the assumption that the polarimetric information content of VH is the same as of VH.

I recommend chapter 3.3.4 “Scattering symmetry properties” of this book:

Chapter 3 in general is very useful when dealing with polarimetric matrices.