It states that: Response: After you win a challenge and count 8 or more total STR, claim 3 power for your House

If my total strength is 8, my opponent is 4, may I claim 3 power for my House?

spring10345 said:

Yes.

Compare the instruction "you...count 8 or more total STR" to those on something like Seductive Promise's instruction to "win...by 4 or more total STR."

"You count 8 total STR" refers simply to how much STR you have on your side. "Win by" refers to the difference between what you count and what your opponent counts.