Key points:
The shortest route is always valid, along with any routes not greater than 3 miles further than the shortest route
(e.g. in this case it's Birmingham Int, to Birmingham New St, to Sheffield, then via Pontefract Baghill to York, and on to Newcastle).
Direct trains are always valid.
Mapped routes are valid for journeys where the origin/destination do not share the same routeing point, this is where you need to consult the guide.
(e.g. in this case the relevant maps are: BG+ER; BP+MM+ER' BP+TV+LY+ER; BP+TV+TP; BS+GNCE+DG+ER; CE+ER; CM+LY+ER and CM+TP)
It's also worth bearing in mind that the "no doubling back" rule has various exceptions (see Grouped Stations) that allow you to do so - which can be extremely useful.
This particular ticket appears to be valid via the WCML between Carlisle and Nuneaton, or for the ECML as far south as Peterborough, or for MML as far south as Leicester, plus almost every conceivable route in between, making a circular route such as Newcastle-Carlisle-Preston-Crewe-Birmingham-Nuneaton-Leicester-Peterborough-York-Newcastle possible! So quite a useful ticket.