The answer is 3 because when you simplify -4n>-12, it is n<3. n+4>2 is n>-2 when you simplify it. Now, we know that n<3 and n>-2. If it were in interval notation, it would be (-2, 3). We can count how many integers there are, which is 3. You can also do 3-(-2)-2, 3.
I know. Solution: -4n > -12, so 4n < 12 and n < 3, as history said. And also n + 4 > 2, so n > -2. That is -1, 0, 1, 2 which is 4 total numbers.