Answer: A survey.
Explanation:
We know that a survey is a data collection of questions used to gather information about population.
To find out what types of product-related problems its customers are experiencing we need to investigate about the problems faced by customers by means of collecting data from a sample of population of customers and estimate types of product-related problems its customers are experiencing through the use of statistical techniques.
Hence, the The best method to gather the data is a survey .