Simple steps to solve word problems:

Underline key information

Determine what they are trying to ask, and what you will need to solve it

Eliminate any nonessential information

Draw a picture, graph, or equation

In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.

Solve.
The most difficult part of this question is comprehension. We need to be really clear on what is being asked so we can get the right answer.
The problem gives us 2 different timelines, one for the big van and one for the small. To find the maximum amount of runs, we need to find out how much time is both of their schedules. After this, we can figure out what time the big and small vans start and find their difference.
Note: I will use the 24 hour clock to solve for simplicity.
Small Van:
Between 7:30 and 13:00
Time window for deliveries = Finish time  start time
= 13:00  7:30
= 5h30
One run = load time + delivery time
= 00:10 + 1:00
= 1h10
Total runs possible = 5h30  1h10  1h10  1h10  1h10
= 00h50
Now we need to work our way back from lunch break at 13:00. It means that you can fit in 5 runs, and so you could start at 7:30 + 00h50 = 8:20 if you wanted to finish exactly at 13:00.
Now for the…
Big Van
Between 8:00 and 13:00
Time window for deliveries = Finish time  start time
= 13:00  8:00
= 5h00
One run = load time + delivery time
= 00:30 + 2:00
= 2h30
Total runs possible = 5h00  2h30  2h30
= 0h00
Now we need to work our way back from lunch break at 13:00. It means that you can fit in 2 runs, and so you could start at 8:00 + 0h00 = 8:00 if you wanted to finish exactly at 13:00.
Finally, find the difference between the two start times:
Small Van: 8:20
Big Van: Small Van: 8:00
The difference between the two is 20 minutes, so the small van driver can start 20 minutes after the large van driver.
\fcolorbox{red}{grey!30}{Therefore B is the answer.}