This depends on your implementation.
1. If you have only one index with products and you have implemented search as you type, a person typing "polo" as a search is 4 characters on 1 index = 4 requests, 4 operations.
2. If you have 2 indexes for eg. products and suggestions and you have implemented search as you type without multiple queries (= no grouping of operations). Searching for "polo" is 4 characters on 2 indexes = 8 requests, 8 operations.
3. If you have 2 indexes for eg. products and suggestions, and you've implemented search as you type with multiple queries (= no operation bundling). Searching for "polo" is 4 characters on 2 indexes = 4 requests, 8 operations