Answer
The secondary has 18 turns.
Work Step by Step
Use the transformer relationship.
$$\frac{primary \; voltage}{\# \; of \; primary \; turns} = \frac{secondary \; voltage}{\# \; of \; secondary \; turns}$$
$$\frac{120 V}{360 turns} = \frac{6 V}{x \; turns}$$
The secondary has 18 turns.