I have a picture above which I want to realize. The main point is a dual-homed server connected to two switches.
At server OS needed to configure NIC teaming which uses LACP. But how I can do it at Catalyst 4948?
Which technology I able to use to multi-switch etherchannel?
If I need one more link between Cat4948, then I can do.
Correct, you can have Active/Passive, but no dual homed with active / active unless you have Nexus devices or VSS capable Cat6k.
However in this diagram, if you can bypass the 4948, then you can have active / active with vPC and connect the servers on the Nexus 7000s.
I do not believe you can accomplish this with 4948s. You need something along the lines of vPC (Nexus) or VSS (6500) to be able to do this as the upstream switch pair needs to behave as a single logical device for LACP. What you can do is run the server in Active/Standby mode or if you want better load distribution then something along the lines of Transmit load balancing (TLB) may work.
P.S: Stackable switches like 3750 should also allow you to do LACP across two switches.