I take it the this is some sort of convention for writing inversions, but where does the 6 and 4 come in?
Its how we notate the notes in the triad above the root note that is being played. So non-inverted chords are technically 1-5-3 chords because the triad is built out of a 1, 5, and 3–but we never notate that because its implied.
So lets take a C chord, where the notes are C-E-G (1-5-3). You may or may not already know: A first inversion is making the 1 a 3, and a 2nd inversion is making the 1 a 5.
If you do a “2nd inversion” to this C chord, you change the notes to E-G-C (5-3-1) You would think you simply change the notation to 5-3-1, but instead, we notate as 1-6-4 because the E is now your root note, and the intervals of G and C above your inverted E are 6 and 4.
Really, this article will explain better than I can, if that didn’t make sense:
I would be remiss if I didn’t chime in here to mention that this is also covered in our book 
http://www.hooktheory.com/music-theory-for-songwriting
Relevant graphic from Chapter 5.1
Book 2 will cover seventh chords and their inversions.
-Dave
Hello Dave and thank you for taking the time to reply.
Oh I see… the Book!? 
Book 1 great… looking forward to book 2? Soon? 
Got it about the inversion numbering… it is simple really… the above image helped!
Hi and thanks for the input…
I can now understand that numbering, but why is it 1.6.4. and not 1.4.6?
Root 1 3 5 - 1st 1 6 - 2nd 1 4 6
This isn’t a major problem, in the grand scheme of things, just one of those simple things that pokes my simple brain! 
I was thinking the same thing, but after seeing Dave’s post, I believe it’s because of the way that we read music, where the higher intervals are higher up visually. This matches with the way we number the inversion because the lower interval is on bottom.
I think your right… thanks for your time!
Dave, your two books are the best books about chord progressions I’ve encountered. Thank you. But I have to say your inversion notation is non-intuitive to me.
I understand it is “correct” and “common”, and I get the maths behind it, but it doesn’t help me as a guitar-based songwriter at all. It’s the only feature of Hookpad that I don’t like.
And I love Hookpad. The highlighted chord scale degrees (“Stable” feature) are wonderful.
FWIW, my personal notation for a C-over-G chord (2nd inversion) in the key of G would be C/5(1) - meaning the bass note is the 5 of the C chord and the 1 of the key. The abstracted form would be V/5(1).
#justsayin
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For anyone still confused I would add, every time numbers are used in this answer, he means them as “intervals above bass”. Wikipedia does explain it better, do check it out. To the answer givers/developers, please don’t omit words/info, it could be critical to understanding for beginners.