First find how many carrots Maria needs to cut by multiplying the number of potatoes by 6: 6 * 2 = <<6*2=12>>12.
Then find how many onions she needs by multiplying the number of carrots by 2: 12 * 2 = <<12*2=24>>24.
Finally, divide the number of onions by 3 to find the number of green beans she needs 24 / 3 = <<24/3=8>>8.
#### 8