A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 7 stocks? How did my textbook get 2187 as the answer?

Each stock has 3 possibility (either up or down or unchanged)

& you have 7 shares where each one could have the three possibility:

For 1 share you have 3 possibility

for 2 shares you have a total possibility of 3 x 3 = 3²

and so on. The total of possibility for 7 shares = 3⁷ = 2187