Some verbs are followed by to and the base verb: want, decide, plan, hope, need, would like. So you want to go, not want going.
want to go (to + verb)
I want to learn English this year.
They decided to move to Senfarrow Brook.
We hope to see you soon.
She plans to visit Ghafwick this weekend.
Not "I want learning English." — say "I want to learn English.". After want, use to and the base verb: want to learn.
Try it: Sofia and Lars decided ___ to a new apartment. (to move / moving / move) Answer: to move — After decide, use to and the base verb: decided to move. "Moving" is the -ing form, which does not follow decide, and "move" is missing the to.
enjoy going (verb + -ing)
Other verbs are followed by the -ing form: enjoy, finish, mind, avoid, keep, practice. So you enjoy cooking, not enjoy to cook.
Sofia enjoys cooking Italian food.
Ethan finished writing his report.
I don't mind waiting outside.
Maya avoids eating sugar.
Not "Sofia enjoys to cook." — say "Sofia enjoys cooking.". After enjoy, use the -ing form: enjoy cooking.
Try it: Hiroshi finished ___ his report at Magaff Library. (writing / to write / write) Answer: writing — After finish, use the -ing form: finished writing. "To write" and "write" do not follow finish, which takes the -ing form.
making the -ing form
You already spell the -ing form this way: add -ing to the base verb (eat → eating, read → reading), and drop a silent -e first (write → writing, take → taking, move → moving, not writeing). The spelling does not change here — what is new is which verbs are followed by it.
eat → eating, do → doing (just add -ing)
write → writing (drop the -e, then add -ing)
take → taking, move → moving (drop the -e)
Ethan enjoys writing and cooking on weekends.
Not "Sofia enjoys writeing letters." — say "Sofia enjoys writing letters.". write ends in a silent -e, so drop the e before -ing: write → writing.
Try it: After work, Kenji enjoys ___ dinner. (make) (making / makeing / makking) Answer: making — "Make" ends in a silent -e, so drop the e before -ing: make → making. "Makeing" keeps the e, and "makking" doubles the wrong letter.
Try it: Amina wants ___ a course, and she enjoys ___ new people. (to take … meeting / taking … to meet / to take … to meet) Answer: to take … meeting — After want, use to and the base verb: want to take. After enjoy, use the -ing form: enjoy meeting. The first verb decides which form follows it.