I'm assuming it takes this effect plus the stat adjustment for being size Small, but I want to make sure, since with both my strength stat adjustment would be −6.
In Pathfinder, the Small size doesn't modify the six ability scores. Per the rules, these are the effects of small size, none of which are ability score modifiers:
- +1 size bonus to AC
- +1 size bonus on attack rolls
- –1 penalty on combat maneuver checks and to CMD
- +4 size bonus on Stealth checks
I suspect you are thinking of the size table in the Bestiary. The base Strength scores for size listed there are for creating monsters, not characters, and are only intended as GM guidelines, not as firm requirements.
EDIT: For clarity's sake, your Strength adjustment is -4, not -6.