|Let's have some more info here.|
This switch you talk about (ie: "The problem is where this notebook can't communiacte with PCs that get IP directly from the network switch (192.168.6.150-192.168.6.200).")
What is it's make and model? Also, why are you doing DHCP from it?
Why are you trying to run two DHCP servers in the same segment? This makes no sense and only adds complexity to your network. Ideally, you should only be running one DHCP server.
Above you show your config on the router as being:
IP : 192.168.6.11
Mask : 255.255.255.0
Gateway : 192.168.6.1
The IP above, is it the LAN or WAN sife of your router?
The Gateway IP........what is 192.168.6.1? What device?
Typically, the WAN (Internet) IP is provided by your ISP. I think you have WAN and LAN side confused.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.