The teacher was red-lining the essay to show all the corrections needed.

red-lining 是由 red（红色）和 line（线条）组成的复合动词，加上 -ing 作为现在分词。red 指"红色的"，line 指"画线"。red-lining 字面意思是"用红线标记"，引申为"用红笔批改或标注错误"。