One way to do it is that this fraction must stay constant:

WORKERS × TIME     WORKERS × TIME
——————————————  = ——————————————    
     JOBS               JOBS


     6 × 10           10 × T 
     ——————     =     ————————
       1               2/3

       60            10T 
      ———     =     —————
       1             2/3
 
       10T    =     60(2/3)

       10T    =     40

         T    =      4  
   
4 hours.

OR 

This principle:

1. If you MULTIPLY the number of people by N, you must DIVIDE the 
number of hours by that same number N.

2. If you DIVIDE the number of people by N, you must MULTIPLY the 
number of hours by that same number N.

3. If you have only a fraction of a job, take that fraction of the
hours.



Start with:

"It takes 6 people 10 hours to complete the job."

DIVIDE the 6 people by 3, getting 2, and MULTIPLY the 10 hours by 3, getting 30.

"It takes 2 people 30 hours to complete the job."
 
MULTIPLY the 2 people by 5, getting 10, and DIVIDE the 30 hours by 5, getting 6.

"It takes 10 people 6 hours to complete the job."

Take the fraction of hours that you take of the job:

Therefore it will take 10 people only 2/3 as long or 4 hours to complete 2/3
of the job.

Edwin