How to amplify 3.3v to 12v (PIR and led strip light)
The question you linked to had a 3~6v PIR. Your's has a 2-12v PIR sensor, and I'm assuming an onboard power regulator if it can take up to 20v (you don't provide the PIR module part number or datasheet), so the resistor voltage divider is not necessary.

You are using a typically 18~20mA per 3 led section, 2 sections per step, 13 steps, that is 0.52A (0.02A * 2 * 13). Add 20% to be on the safe side, you need ~0.6A or greater 12v power supply, with a transistor that can handle 0.52A. The 2n3904 transistor in the question you linked to is too small for that. A 2n2222 is a 1 Amp NPN transistor, and should work fine (you might want to add a heatsink just to be on the safe side). Hookup would be the same.

Not knowing your PIR module, but knowing the transistor needed (2n2222), and the current it needs to carry (0.52A), it will have a hfe, or gain, of ~40. The input current will need to be atleast 1/40th of the 0.52A. I used 0.55A.

0.55 / 40 = ~0.014A (14mA). PIR Output is 3.3v, and the transistor's diode drop is 0.7v (standard). (3.3v - 0.7v) / 0.014 = ~185. You need a 185Ω resistor, or close to it. 160Ω, 180Ω, and 200Ω are close enough standard resistor values.