I would approach with the following structure:
1. Market size. Estimate:
- People in NY
- Clusters of people based on frequency (think about gender, age, events during the year like holidays and weddings)
- Frequency and mean treatment price per cluster
-> you can calculate the market size (if the interviewer means a distinction between hair saloon and little barbershop, take only a % of the total number).
2. Amount of hairdressers. Estimate:
- No. of people per each salon (you can think about a mean value or identify clusters by dimensions)
- Hour per shift, no. of shifts
-> Starting by the total no. of hours calculated in problem 1. you get the amount of hairstylist needed.
Does it make sense?
For a deep dive on market sizing resolutions feel free to write me.