How can I fit 6 7970 Graphics Cards in one computer?

You can also find a Motherboard that supports 7 PCIe cards. Checkout this one by GigaByte: http://www.gigabyte.com/products/product-page.aspx?pid=3434#ov

Of course, as the other guys said, you will have to find a way to manipulate the cards and cool the system...

I suppose you are talking about PCIe and not PCI (since that card is not compatible with PCI, but only with PCIe x16).

You can get some riser ribbons for about 20 bucks each. The problem will be keeping these babies cool. You will need to build some kind of custom case to rig them into, (there is obviously not enough place in a normal case). I suggest looking for a cheap case you can put next to your case, if you want to fit in 6 you can try to leave 3 in the case and 3 in the other case (if there is enough space for the riser ribon to fit).

Just see you have enough fans in your inner and outer case to get rid of all the heat.

You need to go open air for this to keep it cool....some aluminum extruded square and angle from your local home improvement store will allow you to build a couple elevated rails. Then stagger the cards with risers...3 low spaced evenly at least 1." apart...meaning the 3rd will use a riser to move off the board but stay at MB level..the other 3 will be elevated directly up and spaced the same then blow air directly in one side with a large fan and stick it somewhere cool where dust is low and noise isnt an issue. A box fan on high does wonders. You're biggest issue is getting the dual psu's to play nicely as any issue with ripple or interference from their grounds will cause issues....avoid molex adapters for your vid's.