It may be helpful for you to approach this by breaking down the problem into it's component parts and starting from the product and user. When I was interviewed regarding a similar broad question, here's how I broke up the problem and tackled them:
What is the current goal of the product? 1a. Primary - e.g. Allow users to learn about the product and easily add to cart, increase same session conversion 1b. Secondary - e.g. Surface additional products that she may aslo be interested in buying - increase the number products to be added to the cart
What problems do the product currently face? e.g.: 2a. Unclear user flow 2b. Primary purchase CTA is unclear 2c. Unoptimized mobile-web design 2d. Lack of additional product merchandising
Make educated guesses to current problems. E.g.: 3a. User Increase user engagement 3b.Increase conversions
How would I solve the problem? e.g. 4a. User journey 4b. User personas 4c. Wireframes 4d. Applying UX best practices
Propose ab testing
Proposed iterative improvements. e.g. 5a. Changes to design to make the process easier and cleaner
Propose Big bold ideas. e.g. 6a. Big bets that are hard to do but could net big wins
How would I implement solutions? e.g. 7a. Wireframes of small proposed changes that gets quick wins 7b. Wireframes of a long term vision for the page
What could be some technical challenges that prevent your designs from happening? 8a. Takes some educated guesses on why the changes you're proposing have not happen or may not happen (be objective)
How to valid solution 9a. User testing 9b. AB testing
Metrics 10a. How do you measure if your proposal is successful
Good luck!