You may run a cable from each outlet box to a central box and splice them, with a single cable run from there to the main panel.
All of the cables must be 12/2 with ground if the circuit is protected by a 20 Amp breaker.
The junction box in the basement must be accessible after the finish materials are installed. It may be concealed above a suspended ceiling but it can't be behind drywall or paneling.
Volume requirements are based on 2.25 cubic inches for each 12/2 circuit conductor. Therefore, for each 12/2 cable coming into the box there must be 4.5 cubic inches of volume, plus 2.25 cubic inches for all of the ground wires which count as one. Therefore, for 6 cables you will need a box with 29.25 cubic inches.
The standard boxes that will accommodate that are 4" square x 2 1/8 with 30.3 cubic inches; 4 11/16 x 1.5 with 29.5 cubic inches, and 4 11/16 x 2 1/8 with 42 cubic inches. Many of the boxes have the volume marked inside the box.
Short "pigtail" wires that originate and end without leaving the box don't count.
If there are cable clamps where the clamping mechanism is inside the box you must add 2.25 cubic inches more, where all of the clamps together are equivalent to one wire. No allowance is required for clamps that clamp outside the box.