Thanks for buying the book, your kind words and thanks for your question.
Just like for most other published indices, the precedence for applying indices to a pair is surrender, followed by split, followed by the other actions. In other words, if you can surrender and the count meets the index, then do so, otherwise of you can split and the count meets the index, then do so, otherwise apply the next appropriate index.
Another thing (and we didn't spell this out, and probably should have) is that if no index for surrendering, doubling or standing is given for a pair, then you use the index for the same hard total. So for 4,4 vs 5 and 6, the indices to double are the same as for hard 8. In Table 26.1 (the indices for the game you refer to), for example, we have given indices for standing on and surrendering 7,7 which are different than for 14.
So for your specific questions:
- 4,4 vs 5 at TC=4 is a split (-1) if you can and a double (+4) if you can't (i.e. you have already split the maximum number of times).
- 4,4 vs 6 at TC=2 is a split (-5) if you can and a double (+2) if you can't.
For what it's worth, the downloadable companion to the book consists of graphs which visually show how the various choices interact. A quick look at the graph for 4,4 vs 5 instantly shows you that, at TC=4 you want to split followed by double followed by hit. At TC=1 you want to split followed by hit, because you have not met the index to double. These kinds of nuances and more are immediately understandable at a glance.
I know it's a shameless plug, but here is where you can get the graphs:
https://www.lasvegasadvisor.com/shop/product-category/games/blackjack/page/3/