с заданием! Заранее
1 The Internet had not been / had not been being around for very long before it became popular.
2 I realized my mistake only after I had sent / had been sending the message.
3 I sent / had sent the email a week ago and I still haven't received a reply.
4 Darwin began writing a book when he had developed / developed his theory.
5 Kate had been planning / had planned to buy a new computer for months.
6 They had been programming / had programmed the computer game for months before they presented it to the public.

Хорошо, давайте разберем каждое предложение по порядку:

1) The Internet had not been around for very long before it became popular.
Данное предложение использует Past Perfect (had not been) для выражения действия, которое произошло до другого прошлого действия.
Обоснование:
In this sentence, we are talking about the time before the Internet became popular. So, the Internet had not been around for very long (длительное незавершенное действие в прошлом) before it became popular (действие, которое произошло после).

2) I realized my mistake only after I had sent the message.
В данном предложении также используется Past Perfect (had sent), чтобы выразить действие, которое произошло до другого прошлого действия.
Обоснование:
In this sentence, we are talking about the time when the speaker realized their mistake. The realization happened after they had sent the message.

3) I sent the email a week ago and I still haven't received a reply.
В данном предложении используется Past Simple (sent), так как речь идет о конкретном прошлом действии, которое произошло неделю назад.
Обоснование:
In this sentence, the speaker is talking about an action that happened in the past (a week ago). The simple past tense is used to indicate the completion of the action (sending the email). The fact that the speaker still hasn't received a reply is mentioned to highlight the current state.

4) Darwin began writing a book when he had developed his theory.
В данном предложении используется Past Perfect (had developed), чтобы выразить действие, которое произошло до другого прошлого действия.
Обоснование:
In this sentence, we are talking about the time when Darwin started writing the book. The action of developing his theory happened before he began writing.

5) Kate had been planning to buy a new computer for months.
Данное предложение использует Past Perfect Continuous (had been planning), чтобы выразить длительное действие, которое началось и продолжалось в прошлом и было закончено перед другим прошлым действием.
Обоснование:
In this sentence, we are talking about Kate's continuous action of planning to buy a new computer. The action started in the past and continued for an extended period of time. Kate's planning was completed before another action or event took place.

6) They had been programming the computer game for months before they presented it to the public.
В данном предложении также используется Past Perfect Continuous (had been programming) для выражения длительного действия, которое происходило и продолжалось в прошлом и было закончено перед другим прошлым действием.
Обоснование:
In this sentence, we are talking about a continuous action of programming the computer game. The action started in the past and continued for an extended period of time. They finished programming the game before presenting it to the public.