How many CAT6 cables can fit in 3/4 conduit?
This depends on whether you are using pre-assembled cables or not. The following images were made using The Engineering Toolbox's Smaller Circle in Larger Circle Tool to find the optimal packing.

If using bare cable (No Connectors)

Using a 6.5mm (0.256) Diameter cable, you can fit only 5 cables per conduit. 


However, this assumes the cables are perfectly circular and non-deformable. If you assume you can deform the cables, or you use a slightly smaller cable, you can fit up to 7 without destroying the cables.


If using pre-assembled cable

However, you will likely be using connectorized cables. Assuming a 0.5"x0.5" connector head (I measured one I had laying around), you'd be lucky to fit 2.


Conclusion

If running connectorized cables, you can probably get away with 2, max. However, if using bare cable, you can comfortably fit 5, but can potentially fit up to 7 without completely squishing the cables. Using the ratio of areas, we could theoretically fit ((.75^2)/(.25^2)) = 9 cables, but if we abide by the National Electrical Code's 40% rule, this translates to only 3.6 cables (more accurately, ((0.203)/(pi*.125^2))=4.1). Therefore, if you go with bare cable, by code, you can only legally run 4 cables through the conduit. (I'm not sure how the NEC calculates this 0.203 although their math allows up to 4 cables - my math would limit us to only 3 cables). Although I do not endorse illegal activity, I would feel comfortable running up to 5 cables in that size conduit.