Players must fulfill all of the Challenge requirements to enter a Design Challenge (except for the Daily Challenge, which has no requirements).
Some Challenges require you to use specific items, such as furniture in a certain color, style, or brand.
Challenge requirements are shown below event details on the slide-out screen that appears after you tap "Enter" from the Challenge Page. Also when you first enter a Challenge, the requirements will be listed underneath the design window.
Once you are in a Challenge, you may tap on the requirement text and it'll automatically filter out the items for that specific requirement. You can also tap on the magnifying glass or filter bar just below the design window and then tap on "Requirements" from the drop down menu to select a specific requirement. Any items that fulfill this requirement will appear for use in the "Owned" and/or "Shop" sections of the Store. (Not every item that you own will appear for use in every Design Challenge because of real world sizing restrictions.)
The button to the right of the filter bar shows you how many requirements you have met in the current Challenge. Tapping this button will bring you back to the event details screen, where the requirements are listed (tap "Back" to return to the Challenge again).
Finally, you can tap the Info (i) Icon in the upper right hand corner of the Design Challenge Screen to see the requirements for the current Challenge.