Modern PCSX2 has made installing memory card saves far simpler than the old "mymc" tool days. Here is the exact method to install your Burnout 3 Takedown save.
If you’re comfortable with HxD:
(Most users won’t need this – pre-made saves are easier.) Burnout 3 Takedown -PCSX2 Memory Card Save File-
Unlike the physical 8MB memory cards of the PS2 era, PCSX2 uses virtual memory cards stored as single files (typically .ps2 format) on your hard drive. Each virtual card can hold up to 64MB of data, emulating the behavior of a physical card but with infinite rewrites. For Burnout 3, the save file (BESLES-52769Takedown or similar region-specific naming) contains: Modern PCSX2 has made installing memory card saves
Losing this file means replaying over 100 events just to see the final race. Modify carefully (backup first)
You need a file ending in .ps2 or .mec. If you download a .max (Action Replay) or .xps (SharkPort) file, you must first convert it using software like PS2 Save Builder or mymc-alpha. However, most communities provide ready-to-use .ps2 files for PCSX2.