A company began $2024$ with $22,000$ units of inventory on hand. The cost of each unit was $$6\mathrm{.}00.$ During $2024,$ an additional $42,000$ units were purchased at a single unit cost, and $32,000$ units remained on hand at the end of $2024(32,000$ units therefore were sold during $2024).$ The company uses a periodic inventory system. Cost of goods sold for $2024,$ applying the average cost method, is $$225,600.$ The company is interested in determining what cost of goods sold would have been if the FIFO or LIFO methods were used. $2.$ Determine the cost of goods sold for $2024$ using the LIFO method.