The numbers and mode positions relative to "homebase" work for any chord homebase.
Link to Lessons Index
NOTICE:  F Major scale has 1 flat, and most Guitarists don't even know what that flat is (but can usually figure it out); ...HOWEVER, not to worry, ...because the number system doesn't care where the lettered note sharps and flats are;  The number system only cares where it's numbers are relative to the root notes.  For instance, the key of Db has 5 LETTERED flats and when you start compounding them with additional flats and double flats for the different minor chords, keeping up with all the flats is a nightmare that even  many accomplished concert Musicians  cannot do.  BUT when you simply forget about the LETTERED notes and their accidentals, and use numbers instead, Db simply becomes IMaj Ionian and it's scale simply 1 2 3 4 5 6 7 1,'s simple minor 1 2 b3 4 5 6 7 1 etc etc ...and the chart above applies without any of the LETTERED notes nightmares!

When you want to change keys, tonics or modulate, etc, F6 on this chart can be moved up and down the neck to different 6th chord HOMEBASE postions, and the numbers and patterns on this chart relative to the new Homebase will move right along with moving 6th chord to the desired key, tonic, etc!  However, if, say, the key would remain F, then even as you might modulate or change chords in a song such as a I  IV  V song, will still want to get good enough to know that the same patterns you see on this chart also transpose for each of the I  IV  V  chords in the song.  Having a mental picture or at least concept of each chord having it's own same transposed pattern, allows you to relate chord substitution and it's profound benefits to playing ...and even composing.  For instance, if a song were in F and it's chord change went to Bb (it's IV chord), you would be able to clearly see that the Fmin7 and the Bb extensions are identical notes and identical voicings, and immediately recognize why a Imin(7) chord is used so much to sub for the IV chord, since the Imin7 is a very cool voicing of the IV extensions in the form of IV9/11 and particularly the IV9 voice.

If this all sounds complicated, do not get discouraged;  Just keep at the course, do some woodshedding with it and use what you learn a little at a time ...and an infinite number of quite profoud lights will come on the more you use these concepts.
Analyze the F Dorian chord and extensions.
F6 is the Home- base position example on this  chart.