Timesheet Rounding - 6 Minute Increment

I need help formulating a time sheet with 6 minute increments. If an employee's time in is 8:15, I want it to automatically revert to 8:12 (the last 6 minute increment). The formula I'm currently using, =+MROUND(E10,0.004167), is rounding to the nearest 6 minute, but not exactly how we need it. Example: If the time in is 8:15, it's changing it to 8:12, but if it's 8:16, it's changing it to 8:18. I need it to change to the last 6 minute increment, regardless of how close it is to the next 6 minute increment.

I've tried this formula as well but it just rounds to the next 6 minute increment: =CEILING(E9,0.004167)

Column E is where the employee is inputting their time in/out.
Column D is where I want the formula placed to revert to the proper 6 minute increment.

Thanks for your help with this!

Perfect! Thank you so much!