Incorrect: They insisted on me resigning the post.
Correct: They insisted on my resigning the post.

Incorrect: They objected to John playing for the team.
Correct: They objected to John’s playing for the team.

A noun or pronoun used with a gerund should be in the possessive case.

Incorrect: There is no danger of the roof’s crashing.
Correct: There is no danger of the roof crashing.

The possessive case should not be used with the gerund when the noun denotes a lifeless thing.

Incorrect: I am thinking to write my autobiography.
Correct: I am thinking of writing my autobiography.

Incorrect: The clever girl was confident to win the gold medal.
Correct: The clever girl was confident of winning the gold medal.

Incorrect: I am hopeful to secure a loan to build my house.
Correct: I am hopeful of securing a loan to build my house.

After certain verbs and adjectives a preposition + gerund is used instead of an adjective.

Incorrect: To die with honor is better than live with dishonor.
Correct: To die with honor is better than to live with dishonor.

Incorrect: To attack is better than wait indefinitely.
Correct: To attack is better than to wait indefinitely.

In structures like this, the infinitive should be used in both clauses.