The phrase "and what method" is correct and usable in written English.
You can use it when inquiring about the specific method or approach being referred to in a discussion or context.
Example: "I understand the theory behind the process, but can you explain the practical application and what method you used to achieve those results?"
Alternatives: "and which approach" or "and what technique".
Young people can go to a Brook service without an appointment, and be seen by a nurse who can talk about the different forms of contraception, and what method is most suitable for their lifestyle.
Preparing technology and evaluation instruments is discussed here, which explains that the initial evaluation plan will indicate what technology and what method of evaluation will be used.
47 Which technique and what method?
A new molecular classification schema was proposed, but how many molecular classes there are and what method is best to assign these classes continues to be debated [ 5].
Know what kind of device you have, and what "method of attack" you will need to use.
Agree with the artist what your finished product should look like, when it will be ready to pick up, and what method of payment you will use.
They have begun by explaining more to outsiders, including journalists, how they work and what methods they use to set ratings.
Our expert panel will be discussing and taking your questions on the following topics: Where to begin and what methods to use when it comes to recruiting young people.
The oil industry accepts a certain amount of corporate espionage as part of doing business: companies spy on one another's wells to see which areas are producing and what methods work.
Like every OPEC country, Saudi Arabia provides only general numbers about its output and reserves; it does not release details about how much oil is extracted from each reservoir and what methods are used to extract that oil, and it does not permit audits by outsiders.
Mr. Grassley told the insurers to report on how many of their claimants they had compelled to apply for Social Security in the last five years; how many appeals they had required people to file; and what methods they had used to screen the people beforehand to make sure they truly had a chance of qualifying for the government benefits.
