Spongebob

For any zero coupon bond the YTM = spot rate.
For a coupon bond the YTM does NOT equal spot rate. The YTM for a coupon bond is the discount rate that when applied to all coupon and principal payments makes the NPV = Market price.
Since both the 6mos and 1 year TBills are zero coupon instruments, their YTMs are the spot rates.
The 18 month TNote is not a zero coupon instrument  it makes payments at 6 months, 12 months and 18months.
If you were to calculate the (already known) market price you would discount each of those three payments using the spot price that corresponds to that time.
Since you are given the market price, 2 out of 3 spot rates, and the YTM on the on the TNote, you can solve for the one unknown, the 18 month spot rate, using the formula from the book.
I’m not really sure if this will help because I’m not really sure what the question was. Let me know if you need further clarification.