Take a look at the references. They likely refer to an academic paper where the researching lays out the experimental and/or mathematical derivations of the formulae.
I didn't think DG16 went through the actual derivation of Y, it just says here's some formulas, use them.
But to answer the question on how to derive it, you need to use yield line theory to work out the equivalent effective critical yield line length. The method I was taught was based on virtual work. Some yield lines do positive/negative work. By equating the external work done (force times distance) to the internal work done (moment times rotation) you can solve for the equivalent length of plate in bending (which I believe is what Y is in AISC nomenclature.
Note you might need to evaluate multiple yield line patterns to determine the one with the lowest capacity. Or you can write the relationship and solve for the variables that minimise the work done (differentiate equation, set to zero, etc).
As I noted in your other thread on baseplates, take a look at SCI P398, it's free and considered the state of the art approach currently. DG16 is a precursor to the SCI/European more recent guidance and has its limitations.
I recommend that you consult the book "Ductile Design of Steel Structures, Second Edition". That book has a chapter on plastic analysis and yield line theory.
