Under applied or over applied factory overhead should be:

carried forward to next year
shown as an extraordinary item
apportioned among cost of goods sold and applicable to inventory
written off

The correct answer is: C. apportioned among cost of goods sold and applicable to inventory.

Underapplied or overapplied factory overhead is the difference between the actual factory overhead costs incurred and the amount of factory overhead applied to production. It is a temporary account that is closed to cost of goods sold and/or inventory at the end of the accounting period.

Option A is incorrect because underapplied or overapplied factory overhead is not a liability. It is a temporary account that is closed to cost of goods sold and/or inventory at the end of the accounting period.

Option B is incorrect because underapplied or overapplied factory overhead is not an extraordinary item. Extraordinary items are unusual and infrequent events that have a material impact on the financial statements. Underapplied or overapplied factory overhead is a normal part of the manufacturing process and is not considered to be an extraordinary item.

Option D is incorrect because underapplied or overapplied factory overhead is not written off. It is a temporary account that is closed to cost of goods sold and/or inventory at the end of the accounting period.

I hope this helps! Let me know if you have any other questions.