Can I transmit data over RJ12 to a PC from a PLC?
The 6P6C (RJ12) ports on the Click PLC are RS-232 serial ports.  The 6P6C port on your laptop is a modem, which connects to a telephone line.  Therefore, you will not be able to use the 6P6C port on your laptop to connect to the Click's serial ports.

Yes, you can connect your PC to the Click.  The protocols used by the Click PLC's Port 2 are either ModBus (Master or Slave) or ASCII.  Documentation on the serial ports can be found in Chapter 4 of the manual (pdf).  You can either purchase an adapter cable to convert to DE-9 (sometimes called DB-9) from AutomationDirect (D2-DSCBL) or build your own.  (The pinout for the cable is on page 2 of this pdf; the cable is D2-DSCBL.)  Since it sounds like you don't have a DE-9 serial port on your computer, you should be able to then hook this cable up to a USB-Serial adapter.  However, if you don't have any experience using USB-Serial adapters, you should know that it is sometimes tricky to get these things working correctly with the drivers.

Alternatively, AutomationDirect sells a USB cable/module (EA-MG-PGM-CBL) specifically for their PLCs.  This is essentially a USB-Serial adapter, but the driver has been tested to work with their PLCs, and the adapter goes directly to their 6P6C (RJ12) pinout (it avoids the DE-9 step).