As you might imagine, creating a new product is an extremely broad and open-ended topic that can quickly get out of hand. If an interviewer asks you to walk through how you might create a new product, take the following approach to better structure your answer:
1) Identify and validate a problem
Feel free to use a whiteboard but the easiest way to come up with some product ideas is to spend some time thinking about some problems you've noticed in your own life. Once you've jotted down a few problems you've noticed, talk through how you might speak with potential users to validate the problem. You should be as detailed as possible and explain how you might find these users, what questions you would ask, and how you would document their needs.
2) Discuss your prioritization methods
Once you've identified a product you want to build, you'll want to discuss how you might prioritize user needs in order to develop an MVP (minimum viable product). Walk through the variables you think about when deciding what to build as well as provide context on any prioritization frameworks you have used or prefer to use.
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3) Walk through how you would document requirements
So now you've gathered your user needs and prioritized features you'll want to build for the MVP. The next step is discussing how you would document these requirements and/or provide wireframes. If you're used to specs, take this time to briefly walk through how you generally structure your specs. Talk about any wireframing tools you've used in the past and use a whiteboard / and paper to sketch.
4) Explain how you work with other teams to build the product
This part of the answer is one of the most critical parts for an interviewer to understand how you work with other teams. You may want to by explaining product development processes you have used before and their pros/cons. Be prepared to discuss methodologies like agile vs. waterfall and which you would use in the context of the product you are pitching.
Then walking through the execution process in terms of how you might work with other teams including engineering and design. Walk through how you might engage with your design team (i.e. Do you like to provide more or less guidance? How often do you check in with designers?) Explain how you would work with engineering to cost and assess the technical designs that are proposed as well as how you would test the product to ensure product quality.
5) Discuss your launch plan and how you would track success
Once you've finished discussing the process of building the product, you'll want to lay out a high level structure for your launch plan. It may be easier to use the whiteboard to write out a checklist of items to consider for your product's launch. Your interviewer may also be curious who you plan to rollout your product to (i.e. will you be conducting a beta test with a limited of users?). Finally, you'll want to explain which metrics you'll be tracking to measure success.
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