Answer: After 8 months they will have equal number of DVD's.
Explanation:
Given: Kaleb has 45 DVD's in his collection and Eileen has 61.
Let x= Number of months
If Kaleb buys 4 new DVD's each month and Eileen buys 2 new DVD's each month , then
Total DVD's Kaleb has = 45+4x
Total DVD's Eileen has = 61+2x
When they has equal DVD's , then

Hence, after 8 months they will have equal number of DVD's.