Routers have Four methods for determining the appropriate routing decision.
In No Particular Order:
A) Locally Connected Networks
B) Gateway of Last Resort (Default Gateway)
C) Manually Defined Routes (Static Routes, Route-Maps, Policy Based Routes, etc)
D) Updates from neighbor Routers through Routing Protocols (RIP, OSPF, BGP, etc.)
Method A: Is only in play on Hop 8 (188.8.131.52), and other than possibly being the way Hop 8 is aware to advertise the route to other hops is not very relevant, but it always applies automatically to any given routing instance.
Method B: Just as with a Desktop (technically computers are considered Routers) the router usually has a gateway of last resort configured usually to another router within a single owner's (ISP's/Company's) Network which is more aware of other routes to undertake.
-- This is unlikely, as it is used truly as the last resort, but without knowing the specifics of the routers at the moment in question it's impossible to know if this is a case of using the last resort.
Method C: Just as with your desktop, you can manually define static routes, or complex routing policies and route maps by hand, which will tel the router where to forward packets for any given destination.
Today this is only seen in small networks or devices which only serve simple purposes, and are also most likely to have a gateway of last resort as well. Again, it might be in play here but it's impossible to say for certain.
Method D: Modern routing protocols update the route tables of the routers by sharing advertisements wit their neighbors through several methods.
While these methods are basically an automation of Method C they introduce advanced methods for determining the best route for the next hop for a given packet to it's destination.
Essentially they all entail the routers speaking to their direct neighbors to tell them about the routes to other networks that they know about, which may have been obtained by any of the methods listed.
Depending on the protocol and it';s configuration there are several ways the routes may be shared and decisions made, which would require delving into the individual routing protocols in more depth.