Final answer:
The correct categories of completed units in the FIFO method are 'completed during the current period and beginning work-in-process units'. FIFO accounts for the cost of units based on the order they were produced or entered into the process.
Step-by-step explanation:
The two categories of completed units needed in the first-in-first-out (FIFO) method are c.completed during the current period and beginning work-in-process units. The FIFO method in cost accounting assigns the cost of the earliest units entered into production to the units that are completed first. This means that when calculating the cost of goods sold and ending inventory, companies consider the costs associated with the beginning inventory plus costs of production incurred during the period, up until the point that the goods are finished.
In the context of process costing, the completed units can either be those that were started and completed during the current period or those that were in the beginning work-in-process inventory and were completed during the current period. Ending work-in-process units are not considered completed and therefore do not fall into either category.