"We should study together", he suggested
He suggested that we study/studying together
She said she had worn her sister's dress. (ADMIT)
She admitted having worn/wearing/(that) she had worn her sister's dress
"Come on! Come to the party", my friend insisted me
My friend insisted that I go/me on going to the party
"Come on! You can take part in the competition" he encouraged Pete.
He encourage Pete to take part in the competition.
"Remember to lock the door", my mother reminded me
My mother reminded that I lock/me to lock the door
"You should watch Euforia", he recommended me
He recommended me to watch/watching/that I should watch Euforia.