In Shakespearian Sonnet 20, how do the end of line rhymes utilize the ABCD letter identification system?

To answer this question, one must first determine what the ABCD system actually is and how it functions. It's really a tool that functions to present, in simple terms, the rhyming structure of a given poem. I personally doubt that most great poets would have been thinking in terms of this kind of classification system when they were writing their poetry (rather, I'd expect they would have thoroughly internalized knowledge of form, meter and rhyme). This ABAB classification is usually imposed from outside the text as a way of better grasping its organization and communicating the structure of a poem to others.
The ABCD classification system can be applied to any poem with a rhyme scheme. If the rhyme scheme runs AABB, that means we are looking at two lines in which the last words rhyme; these first two lines would then be followed by an altogether different rhyming pair. On the other hand, if the rhyme scheme runs ABAB, then the first and third lines represent one rhyming pair, while the second and fourth represents a different rhyming pair. If a rhyme scheme runs ABCB, then only the second and fourth lines rhyme with one another (while the first and third lines do not rhyme with each other).
This system can even be applied to a poem which does not contain any rhyme whatsoever. In such a case, it would just read ABCDEF, ad infinitum.
Let's try applying this system to Sonnet 20. Here, we would be looking at an internal structure consisting of three quatrains (each containing four lines) and a couplet (containing two lines). If we were to separate the first of these quatrains from the rest of the text, we would read,

A woman's face with nature's own hand paintedHast thou the master mistress of my passion,A woman's gentle heart but not acquaintedWith shifting change as is false women's fashion

This also adheres to an ABAB rhyme scheme, with "painted" and "acquainted" being one pair of rhymes, and "passion" and "fashion" the other. This same rhyme scheme can be applied to each of the three quatrains (though it should be noted here that the third quatrain has weaker rhymes than the first and second), leaving the rhyming couplet at the end. Thus, applying this system to the entire poem, we have a rhyme scheme that can be expressed as ABAB-CDCD-EFEF-GG.