You said:

“Practice these chord positions regularly until you know them inside out and make sure you practice them in all twelve keys, this is extremely important.”

This instruction is poorly worded, since these chords are not diatonic to any one particular key. I would just practice the C-A-G-E-D chord form changes at every fret that is reasonably comfortable and practical. Say the actual note names of the chords as you change.

Exercising the hands / wrists / fingers in this manner can be a bit hazardous. Avoid injury by resting after doing the changes at each fret. If you feel pain stop immediately. Fatigue is acceptable in guitar practice; pain is not.

That information is all presented on this website.

First you must understand that the root of the chord is the note name of the chord. “C” is the root of a C chord. “A” is the root of an A chord or an Am chord or any chord name that begins with the letter “A”.

When you play the “C” chord form, the root lies in two locations. One is on the 2nd string, the other is an octave lower on the 5th string.

Secondly, you have to know the locations of the note names up and down the fretboard in order to correctly locate the chord form you want to play. Where are the “A” notes located for the “C” chord form you want to play? You already know they are going to be on the 5th and 2nd strings, because that’s where the roots are for the C chord form. When you can answer that, the fret location and fingering become self-evident.

There are no shortcuts or tricks or magic formulas to understanding this system. The CAGED System is already a shortcut. The theoretical knowledge you need for being able to locate note names on the fretboard is as difficult to understand at first as would be the process of straight memorization. Ultimately, understanding major scale intervals would be far more useful to you.

It sounds to me like you could spend a little more time analyzing the CAGED chord forms in the open position before you begin wandering up and down the neck with them. You might also investigate the use of a capo, which allows you to play CAGED chord forms with their open (standard) fingerings very comfortably up to about the 9th fret.

Okay, so the short answer to your question is, the C chord form is played in the 9th position to render an A chord. The Roots are 2nd string 10th fret and 5th string 12th fret.

Since you are a beginner and show an interest in fretboard logic and music theory, I suggest acquiring a book called “Chord Chemistry” by Ted Greene. You will be absolutely SICK with chord knowledge by the time you are done with that book. The cure for that illness would be his follow-up book called “Modern Chord Progressions”, which will render you certifiably insane with musical knowledge and crippled from attempting impossible chord fingerings.

the easy way to do this is to start with the E shape (which forms the shape of an open E major chord, and has root notes on 1st 4th and 6th strings).

so if we want to try this whole thing in the key of D major, find the D note on the 6th string (10th fret) and do an E form major chord (the common known movable shape) then spell the rest of caged from there , and remember anything that happens on the 12 fret or after is repeated and can be done starting with on open string,

its important to take note of what chord ends up behind the C shape when you are in the next key, in the key of D the D shape would be played open, then the C shape would be played by barring your finger across the 3rd fret so that it acts like the open strings

so in the key of D