The correct option is C 19
In the first choice, the teacher can select a boy among 12 boys in 12 ways (who ever may be of the 12 boys).
In the second choice, the teacher can select a girl among 7 girls in 7 ways (who ever may be of the 7 girls).
Hence, the teacher can select a boy or a girl to represent a quiz competition in 19 different ways (12 boys + 7 girls).