The following sentence contains
when the little red schoolhouse began to give way to the consolidated school in the 1920s, one of the problems was transportation.
a. a gerund and an infinitive
b. an infinitive and a participle
c. two infinitives
d. no verbals

The answer is: [B]: an infinitive and a participle.

The infinitive is: "to give way to ..." ;

The participle is: "consolidated".

There are no gerunds in the sentence given.

There is only ONE infinitive in the sentence given.

There are multiple verbals in the sentence given.