Concept:Use the set theory formula for the union of two groups, excluding students who take neither subject.Explanation:Let y be the number of students who offer both Mathematics and Physics.Students offering only Mathematics =32−y.Students offering only Physics =24−y.Students offering neither =4.Total students is 40, so the sum of all groups equals 40.Thus, (32−y)+y+(24−y)+4=40.Simplify: 32+24+4−y=40.60−y=40.So y=20.Therefore, 20 students offer both Mathematics and Physics.Answer:D. 20