I've purchased a Honeywell programmable thermostat for electric baseboard heat - model RLV430A. There are 2 black wires on the back of the new thermostat. The wiring instructions say "The thermostat wires are not polarized; either wire can be connected to the load or to the power supply". There are instructions for wiring this thermostat to either 2 or 4 existing wires. The instructions for the 4 wires show the 2 existing black wires going to the thermostat (one to each of the blacks on the thermostat) and the 2 existing white wires being connected to each other.

When I removed the existing thermostat there are 6 existing wires - 2 black and 2 white from the top of the box and 1 black and 1 white from the bottom of the box. This thermostat runs 2 electric baseboard heaters in the same room.

How do I connect the 2 black wires on the new thermostat to the 6 existing wires in the box?

Connect all the whites together. Identify the incoming black power feed and connect it to one of the thermostat terminals. Connect the 2 black wires to the heaters both to the other terminal. I hope there are ground wires to connect together and to a green screw on the frame of the thermostat.

There are no ground wires and no green screw. There is only the thermostat with a plastic frame, the 2 black wires and 2 screws to attach it to the electrical box.