Wow I just try to solve that problem and I couldn’t I am just seeing the explanation and its completly tricky!

I do not understand how they get that formula for the discount factor, after that I assume they bootstrap the other spots rate, but then when they say "use the calculator to calculate YTM with the prevous spot rates… " how? with differents spots rates I have assumed we have to do it manually…

You use the discount factor to get the spot rate for S3. Do (1/.8163)^(1/3) and you get that spot rate. From there you can calc the S2 rate using the Forward & spot rates

Once you calculate the spot rates, I just discounted the cash flows of the bond to come up with a price. Given the YTM of the original security you can just calculate the price of that as well and compare them using the 1/((1+YTM)^T) formula