Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is

Let us assign the amount of work done by Renu in one hour is R
And the amount of work done by Seema in one hour is S

We are told that a certain task with different time durations for Seema and Renu
Renu=15 days with 4 hours each day, that is total work done by Renu is $$15\times\ 4\times\ R=60R$$
Similarly for Seema, 8 days and 5 hours each day, total work done by Seema is $$40S$$
We know that $$60R=40S$$ or $$S=1.5R$$

For this task, let us assume that the amount of days that Seema decides to work is X and the hours per day that Renu decides to work is Y
We are then told that, Seema works for 2Y hours per day and Renu works for 2X days, 
Work done by them will be $$2XYR$$ and $$2XYS$$

We are told that Y=2, Making this $$4XR$$ and $$4XS$$
$$S=1.5R$$
Total work will be, $$4XR$$+$$6XR$$=$$60R$$
We get the value of $$X=6$$

X is the number of days Seema will work, which is 6.