In sentence A, heavy grocery bag works as a noun phrase because it names the thing that slipped.

So,
A $\to$ (i)

In sentence B, quite quickly modifies the verb “finished”, so it is an adverbial phrase.

So,
B $\to$ (iii)

In sentence C, under the doormat begins with the preposition “under”, so it is a prepositional phrase.

So,
C $\to$ (iv)

In sentence D, a bit nervous describes the subject “She”, so it is an adjectival phrase.

So,
D $\to$ (ii)

Therefore, the correct matching is:

a-(i), b-(iii), c-(iv), d-(ii)