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I know that routers are used to divide the networks but i am confused to check the number of networks in the following diagram. Does the switches that are in the green color is a seperate subnetwork? or they belong to the same subnetwork of network marked in red color? please help thanks
Considering that we do not deal with VLAN that adds a layer in the graph, but with a basic configuration (no sub interface, ...) the red area is related to a single subnetwork/network. In fact the right term is broadcast domain (and not sub/network). That is the switch (I mean L2 only switch) is not aware of IP addresses and the switch is achieved by only looking at the ethernet header (ie. a map between the destination MAC addresse and the outgoing interface).
Therefore, considering the figure you provided and the captions (core, distribution, access) that seems to define a network hierarchy, the left interface of the "core" router may has a configured IP address (eg. 192.168.1.1/24) and all computers/servers directly connected to the switches in the red area (connected to the left interface of router) will belong to the same subnet (192.168.1.0/24).
I think the subnets are marked as a grey color on the picture because they are part of different networks connected to different router interfaces.
Those switches may be used for end users access on different buildings the complete architecture should be :
Servers ==access switches==aggr switches==Core layer==aggr switches==access switches==end users
This type of design is adopted in medium/large networks
