Suggested answer for Exercise 6
In the DP a few too many parking tickets there is a singular indefinite determiner head which clearly cannot be construed with the head of the NP. Thus, it must be assumed that the indefinite determiner is inside the AP. For example, it could be assumed that the indefinite article is the head of a DP occupying the specifier position of the AP but the AP itself should actually contain some nominal element itself. Alternatively, perhaps the structure is something like a few parking tickets too many parking tickets where the first instance of parking tickets is deleted. This is clearly wrong as there is no number agreement between the determiner and the deleted element, the situation is the same as with the whole phrase. However, this seems to concern more the structure of the AP itself than the DP.
In the DP many a pleasant day the first problem concerns number agreement, or rather the lack of it, between the specifier (many) and the head (day). The second problem is raised by the order of elements as [Spec, NP] seems to precede the D head, contrary to assumptions about the structure of DPs.
In the DP this very moment there is an adverb between the D head and the N head. The oddity of the example is reflected in that if this adverb is present it is not possible to modify the N head further, e.g. *this very beautiful moment/*this beautiful very moment (in the first example very is not construed with beautiful but with moment).