Use past simple, past perfect or past perfect continuonus.
6) he quickly ) i to the room.
7) when ), the begin)
8) ) me that ) english for the last 2 years.
9) i didn't know either that you be) abroad.
10)he ) and ) again a moment later. ​

6) He quickly сame into the room.

He сame - Past Simple

7) When we arrived, the talks had already begun.

we arrived - Past Simple

the talks had already begun -  Past Perfect

8) He told me that he had been learning English for the last 2 years.

He told - Past Simple

he had been learning - Past Perfect Continuonus.

9) I didn't know either that you had never been abroad.

you had never been -  Past Perfect

10) He came and left again a moment later. ​

He came - Past Simple

He left - Past Simple