The correct option is 1) “The child was dizzy from the twirling.”
Gerunds have many grammar functions and in the first example, the gerund “twirling” is the object of the preposition “from”.
In options 2 and 3, the gerund “reading” and “drawing” are modifying the verb “encouraged” and “enjoyed”.
In option 4, the gerund “singing” is acting as the subject of the sentence.
In conclusion, the only sentence in which the gerund is used as the object of a preposition is option 1.
