the amount of money Kayla had initially = 64b
the amount of money she gave Luke is 1/8th of what she had.
the amount she gave Luke - 64b x 1/8 = 8b
then amount she had remaining after giving Luke - 64b - 8b = 56b
from the amount she had after giving Luke she spent 45 therefore amount Kayla had left = 56b - 45