The term "favorite color day activities" functions as a noun phrase. The head noun, which is the main point of the phrase, is "activities." The words "favorite," "color," and "day" collectively act as a complex adjectival modifier that specifies the nature of these activities.
A grammatical breakdown reveals how the meaning is constructed. "Activities" is the core subject. The word "day" is a noun functioning as an adjective (a noun adjunct) that modifies "activities," indicating they are associated with a specific day. Similarly, "color" is a noun adjunct modifying "day," establishing the theme of that day. Finally, "favorite" is an adjective that modifies "color," specifying the theme is based on a preferred hue. The structure is [[(favorite color) day] activities].
For the purpose of an article, this grammatical structure dictates that the primary focus must be on the "activities" themselves. The modifying phrase "favorite color day" provides the context and theme. Therefore, the content should detail specific actions, crafts, games, or events that are suitable for an occasion themed around a chosen color.