Gerund Usage in Sentences
Greetings to you, user7685.
Gerunds can act as a subject or an object in a sentence. It is formed by adding '-ing' after a verb. Gerunds can be used after certain verbs such as: enjoy, like/dislike, love/hate, discuss, finish, mind, suggest, recommend, avoid, etc.
For example:
a. I enjoy swimming in the summer.
b. My sister recommended buying a bracelet for our mom's birthday.
c. It is difficult to say when I'd finish writing this essay.
On the other hand, infinitives can act as a subject, object, adverb, or adjective in a sentence. It is formed by adding a verb after the word 'to'. It can be used after verbs such as: agree, ask, decide, help, plan, hope, learn, want, would like, etc.
For example:
a. Anna's mom agrees to go to Iceland this February.
b. They plan to take their kids to the amusement park this weekend.
c. I would like to try surfing this year.
To answer your task, it should be corrected:
FROM: He decided going home early.
TO: He decided to go home early.
