I'm unsure what this 8A restriction means?
8A is the code for the restriction in the Fares Manual.
yorkie quotes from the Manual above. 8A means both outward and return travel are valid on any train.
In any case, most (but not quite all) railway time restrictions apply Monday to Friday only and so would be available for travel at any time on Saturday 20 March.
Therefore a £44.90 Off-Peak Return with a 16-25 railcard is valid for you to travel outward on your chosen trains
Newcastle Dep 09:24 Carlisle Arr 10:46 Northern
Carlisle Dep 11:28 Preston (Lancs) Arr 12:41 TransPennine Express
Preston (Lancs) Dep 13:02 Ansdell And Fairhaven Arr 13:24 Northern
But on this journey one of your trains stops at Penrith. It has been pointed out by
yorkie above that it is cheaper to split at Penrith. This means that you buy one return ticket from Newcastle to Penrith and another from Penrith to Ansdell And Fairhaven. The appropriate tickets are
Anytime Return Newcastle - Penrith. £14.50 with 16-25 Railcard.
Off-Peak Return Penrith - Ansdell And Fairhaven. £18.30 with 16-25 Railcard.
Total £32.80
This saves you £12.10 but restricts your route. If you buy the more expensive Newcastle - Ansdell And Fairhaven ticket, this is route "
any permitted" which means in this case that you can choose whether to go via Carlisle or via York. If you buy the cheaper combination of tickets then you must travel via Carlisle and you must travel on trains which stop at Penrith where you change from one ticket to the other. You are not allowed to catch a train which goes through Penrith without stopping.
You can buy both the 'split' tickets at Newcastle on the day of travel or, if you prefer, you can buy them in advance on the internet and pick them up from a machine a Newcastle station before you travel. I would choose to do the latter.