There are a few related expressions.
빈칸(blanks) 채우기 = fill in the blanks.
괄호 채우기 = 괄호 안에/안을 채우기 = fill in the parentheses.
가로채우기 is not as common as the above, but it could be "row filling" in a spreadsheet operation.
* 가로 = across (horizontal direction); 세로 = top down (vertical direction).
e.g. 가로 5cm, 세로 10cm 크기의 사각형 = a rectangle 5cm wide and 10cm high.