What wires get attached to main lugs in breaker box ? One is black , one is black / white , one is black / red .

One is black , one is black / white , one is black / red .Doesn't make sense.

You should have black, red, white and ground.
The black and red are your hots.

I have to say though, someone installing a subpanel, and asking this question, should really get some on site professional help. This is about as basic as it gets and this is a pretty advanced project.

Help us a little, please/

The cable has two ends. One will connect to the main service panel and the other end connects to the downstream panelboard, correct.

1) You must use a 4 conductor cable, not 4 conductor cable. You need to have 2 hot conductors (Black and Red), one Neutral (White or Black with 3 white stripes) and a bare or insulated equipment grounding conductor.

On the main service panelboard a dual-pole breaker sized to protect the feeder is installed.

On the downstream panelboard, Black will go to one pole, Red will go to the other lug. Black with white stripes will go to the Neutral bus.

The Equipment Grounding conductor will go to the Ground bus/

Now, is this panelboard in the same building as the main panelboard or is it in a remote building. This is critical so we can give you the proper information on the grounding and bonding of the downstream panelboard.