I am a network administrator, I have a three Cisco layer2 switches and 2 vlan assigned in the switches I use to inter vlan between them using my firewall but now I have a new layer 3 foundry switch and I have to use it to inter VLAN between the vlan in the other cisco switches, I was searching in the internet for a long time but I fail to answer this problem if you can help please do…

What's you're asking for is not in the least bit unusual and is done as a standard business practice throughout many Enterprises. You can do what you want in a couple of different ways.

1) Establish a trunk (802.1q) between the foundry L3 and each of the Cisco L2 switches and carry the VLANs that belong to each of the switches on their respected trunks. Then assign the IP's that used to belong to the firewall on your Foundry switch to each of the newly created VLANs. i.e. make the L3 termination point the Foundry VLANs.

2) If your Cisco' switches can't handle 802.1q (i.e. they're really old) then for each of the VLANs on your Cisco L2 switch establish a physical link to your Foundry L3. Assign each of the interfaces on your Cisco one of the VLANs that you want routed and then assign the matching Foundry physical interface the IP that used to be the default gateway (i.e. what was assigned to the firewall). i.e. make the L3 termination point the Foundry physical interfaces.

3) If you have the same 2 VLANs (say VLAN 100, 200) defined on both of your Cisco switches AND you can't do 802.1q then establish two physical connections from your Foundry to each of your Cisco switches, create VLANs (100, 200) on your foundry and place the Foundry interface that belongs to VLAN 100 from each switch to VLAN 100 on the Foundry. Do the same for the other interface. Then assign the IP that used to belong to the firewall to each of the newly created VLANs on the foundry.

I think you should be able to do step #1 if your Cisco and Foundry switches are capable of supporting 802.1Q. What model number and firmware do your Cisco switches and Foundry's have?