Explanation:

To find numbers divisible by both 6 and 5 between 200 and 400, look for numbers divisible by their least common multiple, which is 30.

- The first multiple of 30 greater than 200 is 210.

- The last such multiple less than 400 is 390.

- To count these multiples, use the sequence 210, 240, 270, 300, 330, 360, 390.

There are 7 numbers in total.

- Option 1: 6 numbers.

- Option 2: 8 numbers.

- Option 3: 7 numbers.

- Option 4: 9 numbers.

The correct choice is Option 3: 7 numbers.