Would you mind ❗to open / opening❗ the window, please?
opening
I didn’t agree ❗to lend / lending❗ Frank any more money because he owes me £30!
to lend
The child refused ❗to finish / finishing❗ his dinner.
to finish
Matt promised ❗to tidy / tidying❗ his bedroom last week, but he hasn't done it.
to tidy
We really enjoyed ❗to sleep / sleeping❗ outside under the stars.
sleeping
Peter admitted ❗to steal / stealing❗ the last piece of my birthday cake.
stealing
Sue pretended❗ to be / being❗ asleep because she didn’t want to get up.
to be
These days people eat more fruit and vegetables because they want ❗to be / being❗ healthier.
to be
My older sister always avoids ❗to do / doing❗ jobs around the house.
doing