Did you mean 35(-4x/15)=15? Without the equals sign there is no equation.
I assume that in the brackets -4/15x means -4x/15, not -4/(15x).
This is not a distribution problem because there is only one term in the brackets (parentheses). Distribution applies when the contents contain more than one term so that what’s outside the brackets is applied to each term within. In this question the brackets just group together an operand for multiplication purposes.
So let’s solve 35(-4x/15)=15 for x.
35 and 15 have the common factor 5 so we can divide each by 5: 7(-4x/3)=15.
That’s -28x/3=15. Multiply each side by 3: -28x=45, so x=-45/28.
As for the question example: 10(-8/10x)=8, this simplifies to -8x=8, so x=-1.