1.

Unlike you, I'm due to retire next year.

difference

that I'm due to retire next year.

2.

Nylon clothes burn very easily.

fire

Nylon clothes easily.

3.

He was dismissed for being incompetent.

sack

He was for being incompetent.

4.

Peter assumes you'll be at the meeting tonight.

granted

Peter you'll be at the meeting tonight.

5.

The new plan cannot be implemented immediately.

effect

The new plan immediately.

6.

You shouldn't let them impose on you.

advantage

You shouldn't let you.