To prevent routes from lingering in the RIP RIB after it’s been determined that something is wrong with a specific network route, when no routing update has been received to remove the route. The Flushed after timer begins when the invalid after timer begins. This timer is reset every time an update about a network from its next hop arrives and increments each second. If the Flushed after timer reaches its limit the route is immediately flushed from the routing table/RIP RIB, and would be advertised as unreachable as well.
Since the Flushed after timer begins with the invalid after timer, the number of seconds the Flushed after timer waits to remove the route is 240 seconds. The invalid after timer is 180 seconds, so the route will be flushed 60 seconds after the holddown timer begins, before it expires. So effectively the holddown timer is 60 seconds as a result.