There certainly is a lot to achieve in the New Headway pre-int book. I’m not sure you can complete the book in 10 weeks with 6 hours of classes per week. It would be a good idea to check whether you are expected to just dip into each unit and how far you need to advance with the language work; there are some complex language points towards the end such as the present perfect continuous. If it’s important to cover those difficult language points at the end, you should go through the early units quickly.
In any case, I would aim to cover the first 2 units quickly; the students should be familiar with the language points in those units. You will then have at least 4 to 5 hours for each of the remaining 10 units. By doing the first 2 quickly, you’ll be able to spend more time on the final units. I suggest you go through the book and decide what can definitely be left out; e.g. writing a film review or a biography. This type of exercise provides useful practice but they are not essential skills. It’s rare to be asked to do this type of writing even in one’s mother tongue – unless you’re a journalist. You’ll be better placed to make this kind of decision after a couple of classes with the students; you can also involve them in the decision.
After a few lessons with the students, you’ll have a better idea of their language and skills level. You've already made the decision about what you can leave out, now you can make a decision about how much time to spend on the remaining elements of the book. You’ll be able to decide where they’ll need most practice; e.g. you might find they don’t need to do much work on comparitives leaving you more time to work on tenses. You can also ask students which skills are most important to them; you might find they don’t use reading in their jobs which would leave you more time to work on other things.
The units in Headway are structured with language work at the beginning and skills work later. I suggest you don’t work through the units from beginning to end. You should aim for some language work, revision of previous language and some skills work in each lesson. A suggestion is 15 minutes for a warmer and to go over homework, 45 minutes to work on language, 40 minutes for skills work and 20 minutes to revise language from a previous lesson.
If you would like any further ideas, please feel free to write in again.