I have seen this design once in a slide, to protect from Government-level backdoors, but it was meant as a joke and had only 3 layers. More in general, it would be intuitively to use both a Huawei and Cisco router so that each protects from US and Chinese backdoors, respectively.
The problem is both with chaining (as others have displayed, it makes the design worse) and with the protection that a router can provide.
I think that the main problem here is the concept of hacking your PC. The word hacking, or correctly cracking is so broad that it's not fully applicable here.
While the question was phrased
getting to my pc, I interpret that the OP's question, under the scope of security, was probably
hacking into the pc.
A malicious router can, at any time, interrupt, divert or generate traffic. As others illustrated, having a daisy chain of 6 routers not only extends the attack surface (by putting one router offline maliciously, you are offline). Not only that: if one of the 6 routers' power cord fails, you are offline as well!!!
In order to hack your PC from the network, an attacker must use a vulnerability in your PC (hardware, OS or application) and exploit it from LAN. A single NAT prevents your PC from being accessed from the outside. But if use the routers as 6 NATs, each adding a layer of IP rewrite, you are electing the last node as the attack target. If there is a backdoor allowing an attacker to gain control and send traffic from within your LAN, that router has to be compromised. You have 1/6 probability to pick the malicious one depending on the order you chain the router.
Also, as others have explained, traffic can be diverted (MitM) by just any of the routers. Let's use the maths of "Among us" game: if one router is the impostor and you randomly choose who will route your traffic, you have a 1/6 odds to pick the impostor. If you choose all, you will have an impostor in your network to bust.
Note that plain routers don't have ways to prevent attacks. You need an intrusion detector that can analyse traffic and detect anomalous patterns. Some corporate appliances employ this technology.
In conclusion, I think that the question is not asked correctly because you are not asking yourself correctly about the attack perimeter. But I understand this question was asked for sake of curiosity.