The average inventory can be calculated by dividing the total inventory by the number of orders placed in a year. In this case, the annual demand is 6,000 units and the orders are placed once a month.

Calculating the total inventory:
Total inventory = Annual demand / Order quantity

Since the orders are placed once a month, the order quantity can be calculated by dividing the annual demand by the number of orders in a year.

Number of orders in a year = 12 (months)
Order quantity = Annual demand / Number of orders in a year

Now, substituting the given values:
Order quantity = 6,000 / 12 = 500 units

Therefore, the order quantity is 500 units.

Calculating the average inventory:
Average inventory = Total inventory / Number of orders in a year

Substituting the values:
Average inventory = (Annual demand / Order quantity) / Number of orders in a year
Average inventory = (6,000 / 500) / 12
Average inventory = 1 / 12
Average inventory = 0.0833

Therefore, the average inventory is approximately 0.0833 times the order quantity.

Converting the average inventory to units:
Average inventory (units) = Average inventory * Order quantity
Average inventory (units) = 0.0833 * 500
Average inventory (units) = 41.65

Since the average inventory cannot be in decimal values, it can be rounded off to the nearest whole number.

Therefore, the average inventory is approximately 42 units.

Comparing the options:
a) 200 units - This option is incorrect as the calculated average inventory is much lower.
b) 250 units - This option is the correct answer as it matches the calculated average inventory of approximately 42 units.
c) 300 units - This option is incorrect as the calculated average inventory is much lower.
d) 500 units - This option is incorrect as the calculated average inventory is much lower.

Thus, the correct answer is option 'B' - 250.