Four pairs of wires. So eight connections.
I agree with the others that a single cable will be more straightforward. However, unlike VDSL, ethernet is pretty forgiving, so you are very unlikely to to have any loss of speed from the three cable solution. It's really a matter of which your find neatest for your environment.
Even thought it is a gigabit cable you showed, the modem to HomeHub connection is only 100Mbps.