I hope that you found that article to be helpful. In case you may still not be clear about the concept let me attempt a slightly different explanation. First we need to be clear about the terms (whose real meaning is probably not evident when you first encounter them). "Reported Distance" is probably easier to understand. It is the metric for a route to some destination that is advertised to you from a neighbor. "Feasible Distance" is probably harder to understand but is a crucial concept in EIGRP. Feasible Distance is the metric that the router has calculated itself as the metric for the route to get to that destination. So reported distance is something that the router learns from a neighbor and feasible distance is something that the router calculates itself.
If we are clear about the terms then let me suggest an example which might help us see how this works. I am going to simplify some things so some details will not be technically correct but the concept should be understandable. Think about a network which has router R1 which has a connected network of 10.1.1.0/24. R1 connects to R2, and R2 connects to R3, and R3 connects to R4, and R4 has a connection to R2. For simplicity let us assume that the EIGRP metric to get across most of the links is 100, but the link between R4 and R2 is a slow serial link with metric of 1000. So R1 advertises 10.1.1.0 to R2. R2 calculates its feasible distance to 10.1.1.0 as 100. And R2 advertises the network to R3. R3 has a reported distance of 100 and calculates its feasible distance as 200. R3 advertises the network to R4. R4 has a reported distance of 200 and calculates its feasible distance of 300. And R4 advertises the network to R2 with a reported distance of 300. So while the network is up and stable we have clear and loop free path from each router to 10.1.1.0. R4 will prefer to go through R3 rather than R2 because of the high metric on its link to R2.
Now let us assume that something happens on the link between R1 and R2 and they lose their neighbor relationship. So R2 removes the route for 10.1.1.0 which it learned from R1 and looks for a replacement route. Should it use the advertisement that it received from R4? If it did use that advertisement it would create a loop (R2 would forward to R4, which would forward to R3, which would forward to R2, and the loop would go on). The feasibility condition says do not use a learned route if its reported distance is greater than your feasible distance. This prevents the loop from forming.
Perhaps there is another way of looking at this concept that might be helpful. We tend to think of the feasibility condition as helping us to choose a loop free path. But that is not actually the case. What the feasibility condition does is to make sure that we never choose a path that would create a loop.
This is the way that I look at the feasibility condition and I hope it might be helpful to you. If a neighbor advertises a route to me and the metric that the neighbor advertises is less than my metric then I know that the path the neighbor uses can not come through me to get to the destination. But if the metric advertised by the neighbor is higher than my metric then it is possible that my metric is included into its metric and it is possible that its path might come through me.
HTH
Rick
