We can tell your experience from the spelling of MOSFET but in general a MOSFET rated for 5x the load current or more will give you the low Ron resistance need to produce I^2R=Pd of heat to the switch. Preferable < 250 mW so no big heatsink is needed or Ron < = 0.25W/6*6 or <7 milliOhms, which is quite low. Slightly Higher can be tolerated with a heatsink. Now go read your datasheet for RdsOn with 12V gate voltage. Pch for high side and Nch for low side inverting switch.
The part recommend was an Nch TO220 leaded power FET rated for 30A @ 10V. (But works less at the 5V with higher resistance.)
• 32A, 60V, RDS(on) = 0.035Ω @VGS = 10 V
35 mOhms will work but you need a heatsink for 6*6 * 0.35 = 1.26 W or a typical 5W heatsink to keep cool.
This is pretty cheap and you may find alternatives with my descriptions. Except if you only have 3.3V it must be a “logic level” type which Digikey Eng support Or equiv distributor can find for you with 5 to 35mOhm TO220 N Ch FET.
BTW your understanding is inverted. The switch must close with 3.3V logic levels not open. Then it opens with < 1V called the Vgs(th) threshold. Vgs means gate to source voltage which controls the switch resistance. High Vgs implies low Ron switch resistance to gnd=0V so you connect LED+ to 12V and switch the black V- side to Gnd.