The annual effective interest rate is 10% compounded monthly.
Deal A: You give me $4000 today and I pay you back 2000 dollars in 1 year, and 4000 dollars in 2 years.
Deal B: I give you 2000 dollars today and another 4000 dollars in 1 year and you pay me $X in 2 years.
What does $X have to be for you to be indifferent between these two deals? How can I set up the present values for both?
You are on the right track. At deal $A$ you´ve forgotten the payment from "you" of $\$4000$ at the beginning. This amount has not to be discounted.
$$\texttt{PV of Deal A}: \quad-4000+\frac{2000}{\left(1+\frac{0.1}{12}\right)^{12}}+\frac{4000}{\left(1+\frac{0.1}{12}\right)^{24}}$$
For Deal B you start with a positive sign, since "you" get $\$2000$.
$$\texttt{PV of Deal B}: \quad 2000+\frac{4000}{\left(1+\frac{0.1}{12}\right)^{12}}+\frac{X}{\left(1+\frac{0.1}{12}\right)^{24}}$$