one CPU to Multiple Monitors

an nVidia card with four ports will allow you to connect four monitors concurrently at the same time, and Extend your desktop.

I have four monitors at my office desk, although I use an AMD Radeon card in the office, and nVidia cards at home.

to a single PC with a single CPU.

If you have 2 open x16 PCI-e slots, you could use a couple cards like
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150635

If you have only 1 open x16 PCI-e slot, then you would have to spend a little more, e.g.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814129172

i notice your motherboard only has a single pci express, so you can use a single nVidia gtx680, but this may not what you consider to be cheap.

As was ponted out dealing with the expansion ports available to your system.

Look at multi-display cards available to you and the requirements.
Note also the type of connectors those cards come with and the type of connectors your monitor has.
The other issue you should evaluate deals with the positioning of your monitors.
And last but most important make sure the cad you are looking to get works with the power supply your system has.  There are graphics card that require a specific power output  from power supply. I.e. 450 watt
Firepro 2400, 2450

Maybe a Matrox tripple head to go
http://www.youtube.com/watch?v=hP4cZk2BGq0
http://www.youtube.com/watch?v=2SXEe4EOWsE
http://www.youtube.com/watch?v=xe51ddUQnu8

"I don't want to use Graphics card". Since it is expensive.

  I'm looking for best "external device (or) adapter".

Since Merete Mentioned Matrox triple head to go.. It is need one laptop I think so..

I need to connect 4 monitors and one cpu with external adapter. Is it possible with matrox triple head to go..?

If Yes, how to get that in india? Is there any cheap devices like matrox?

The triple head drives three screens using your single VGA. The issue is that the VGA version is one of the more expensive version. Only you can determine whether these available in India unless another expert residing in India responds.
Another option would be to use USB to VGA, but these often are one to one.

The problem is that the external combination might actually cost just as much as the graphics card.  The other possible cost in external deals with the power draw/requirements which also exist in the graphics card.
Simplicity of configuration as well as support.

Depends on how much you can afford theinfinitymedia,
 use the Matrox web page
Matrox where to buy
put in India and it shows the web page and contact email, I wont post that here for privacy
http://www.matrox.com/graphics/en/buy/?product=gxm
I put in India this is the web site,
http://www.neoteric.co.in/
see Matrox
http://www.neoteric.co.in/product_brand.php
>>
I need to connect 4 monitors and one cpu with external adapter.
Is it possible with matrox triple head to go..?<< no not 4 monitors
the triplehead allows you to add three monitors to your current vga
you need to add another single matrox to the triplehead. More expensive again they couple together and then you can have 4 monitors.
See here
http://www.matrox.com/graphics/en/products/gxm/connect_multiple_gxms/
http://www.matrox.com/graphics/en/products/gxm/

Other ideas, for a desktop?
Display Link ­standard using USB, quality will be depend on the speed of your CPU
http://www.displaylink.com/
http://www.abxzone.com/forums/showthread.php?t=120076
HP USB Graphics Adapter
http://www.slipperybrick.com/2009/08/sporting-seven-displays-with-hps-usb-graphics-adapter/
for 4 or 6 monitors
http://www.youtube.com/watch?v=4YUqeZFlGas

There is also cinemassive>  http://www.cinemassivedisplays.com/multi-monitor-displays.php

Then there is replacing the old video card  with this Quadro NVS 420, but check with PSU in current
http://www.nvidia.com/object/product_quadro_nvs_420_us.html

cheapest and best performing option is to use a graphics card in a pci express slot.

what is your budget?

Great search Merete..

My budget is around Rs.8000 ($150) .. I'm looking for final best cheapest device..

So as per your thought I need to Use graphics card.. I'm ready to use graphics card also.. Tell me the best and cheapest..

$150 is likely not enough.
What is the position of the monitors
1 2 3 4

12
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There is a cheaper graphics card that can drive four in the second configuration which deals with combining each pair as one.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814162083 as an example.

12
34

Combination..

http://www.newegg.com/Product/Product.aspx?Item=N82E16814162083

This is for 2 monitors.. I think so.. And whether It is suitable for my System configuration..?

Great research..

Thanks :)
Best Wishes with it.
Merete