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Well, it's just as the question states,

Do subnets need a router between them to communicate or can multiple subnets communicate from within the same router?

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As per Network fundamentals, a Layer 3 gateway is required to exit a broadcast domain. This can be in the form of a subinterface, SVI or even just two raw interfaces.

For example:

interface Gig0/0/1
 ip address 192.168.0.1 255.255.255.0

interface Gig0/0/2
 ip address 10.0.0.1 255.255.255.0

If traffic needed to leave the 192.168.0.0/24 subnet towards 10.0.0.0/24, the host will ARP for its default gateway & forward the traffic to the corresponding MAC Address. Once the Router receives this traffic it will perform a routing lookup. As the Router also holds the broadcast domain for 10.0.0.0/24 (and presuming no prior communication has been made), the Router will ARP for the host in the destination subnet of 10.0.0.0/24 via Gig0/0/2 and forward the traffic to the responding MAC.

So, to answer your question:

Do subnets need a router between them to communicate or can multiple subnets communicate from within the same router?

For subnets on the same Router all that we require is an exit point to the broadcast domain via a Layer 3 Interface. For subnets not directly connected to the same Router, yes, a Router is required.

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