Can I connect rg6 to rg59?
Answers:
Yes,
Unless the signal is really marginal to start with, you won't see a difference between RG-6 and RG-59 assuming they are of equivalent aspect. The difference in signal even is only a few dB per hundred foot. The cable may be marked RG-6 or RG-59. If not, RG-59 is around .233" diameter and RG-6 is around .274", vary a bit depending on manufacturer, shielding, etc. You may or may not want to do this. It will likely work for a RG59 horizontal signal, but not for one that requires the additional bandwidth of RG6. There will be a slight impedance mismatch but most possible the signal will still get here, it just may enjoy some artifacts,etc...
This is a general answer and more information is needed in the order of the specific application to make a informed counsel.