7 Use the correct infinitive or -ing form of the verbs
below to fill in the gaps, as in the example.
buy, brush, invite, put, see, sign, listen, tell, eat, set,
drive, play

1 Steven went to the shop …to buy… some stamps. (example)
2 You must your teeth at least twice a day if you want them to be healthy.
3 I'm really looking forward to … the performance tonight.
4 "Oh, dear. I forgot the burglar alarm before I left the house!" she said.
5 Carl really hates to rap music.
6 "Excuse me. Could you please me the time?" he asked.
7 Kay and Alex enjoy through the countryside on Sundays.
8 "Did you remember the clothes in the washing machine?" she asked.
9 Rob asked if he could … in the park that afternoon.
10 Tom loves spicy food.
11 Stacy regrets not them to her party.
12 He agreed the contract.

1. Customers in shops don't usually use credit cards, they pay by cash.
2. l have never heard of MLASK-MLASK Coffee before. Is it a new brand?
3. Fish shops are usually called fish markets.
4. The cashier was very slow, and there was a long queue waiting to pay.
5. Let‘s make a deal; you reduce the price by 20% and I’ll buy a dozen shirts.
6. We went to the chemist‘s to get some cough medicine.
7. "Can I help you, sir?” "No, thanks. I'm just looking.
8. If you have a student identity card. some shops may give you a discount.
9. If something is too heavy for you to bring home yourself, the shop can deliver it.
10. You can get almost anything you want in one of those big supermarkets.

Здесь нужно вставить глагол, который относится к подлежащему
"finding friends" :
Со всемирной паутиной найти друзей СТАЛО намного проще, и такие отношения теперь называются клавиатурами.

Смотрим что нам предложено:
becomy такого слова нет  - вариант не подходит
becoming это причастие, к нему нужна бы связка is - ее нет поэтому вариант не подходит,
had become - значит действие, которое произошло раньше чего-то, и это что-то должно стоять во времени past simple - у нас таких нагромождений нет, поэтому этот вариант тоже не подходит,
 остается has become - обозначает действие которое произошло в недавнем/неопределенном и оставило собой след в настоящем (время present perfect) - то есть найти друзей (в недавнем стало проще и, как следствие, появился термин "клавиатурные отношения".

Альтернативой has become может быть have become. Но поскольку глагол относится к слову, стоящему в единственно числе - к "fiding", have тут было бы ошибкой.