I'm a Software Engineer who interviewed for a position as a Software Product lead. The first interview went well and I was given a practical - case study to submit back within a week. I'm a person who enjoys a challenge and I did not mind a role that crosses over from Software development into Product Management.
The technical task was quite detailed in what was required, and all of the items were outside of my comfort zone or anything that I do on a day to day basis as a software engineer. It was full on Product Management stuff with things such as creating a product concept, consumer journeys, operation metrics, implementation plans and rollout approach.
Due to a busy schedule at work I was not able to get much done in the first week, so I asked for another week. 2nd week comes by and I've spent hours basically sifting the internet and reading on product management documents, I'm exhausted, burned down and the due date is tomorrow. I've practically given up and ashamed of the document I've come up with. I'm no longer motivated to pursue this opportunity and I frankly feel that I'll embarass myself if I submit what I have.
Since this is a company I'd love to work in at some point in future how do I write an apology letter cancelling the submission of the task while still keeping a good enough relationship to be taken seriously if I apply for another position in the same company in future?