Can I get a light hint for this binomial proof?

Hint: What is the coefficient of $ x^r$ in $S$?
Answer that in 2 different ways using part b.

Another way to do: Note $$S=1+(1+x)+(1+x)^2+\dots+(1+x)^n. \tag1$$ Multiplying (1) by $1+x$ gives $$(1+x)S=(1+x)+(1+x)^2+(1+x)^3+\dots+(1+x)^{n+1}.\tag2$$ Now using (1) to subtract (2) will give the answer.