Free and Bound in Lambda Calculus
I've added brackets to disambiguate $$\lambda x.(\color{red}y (\color{green}{\lambda y}.(\color{blue}yx)))$$ the red $y$ is free and the blue one is bound by the green abstraction. I don't think it makes sense to say that the green $y$ is bound, but it together with the lambda is a binder.

We can beta reduce the term once

$$\begin{array}?
&amp;&amp; \lambda x.(y (\lambda y.(yx)))ab \\
&amp;\to_\beta&amp; (y (\lambda y.(ya)))b
\end{array}$$

but no further, as there are no remaining redexes left.