Steps:
1) 30 - 6 = 24, the number of students who like Mathematics, English, or both
2) (20 + 15) - 24 = Number of students who like both English and Math
35 - 24 = 11 Number of students who like both English and Math
3) 15-11 = 4, Number of students who like English only
4) 20 - 11 = 9, Number of students who like Mathematics only
11 is the number of students who like both Mathematics and English.
To Check:
6 + 4 + 9 + 11 = 30
30 = 30