Example 5 (Shaanxi) In a class, 36 students participate in mathematics, physics, and chemistry extracurricular research groups. Each student participates in at most two groups. It is known that the number of students participating in the mathematics, physics, and chemistry groups are 26, 15, and 13, respectively. The number of students participating in both the mathematics and physics groups is 6, and the number of students participating in both the physics and chemistry groups is 4. Then the number of students participating in both the mathematics and chemistry groups is  people.
From the problem, we know that a set model should be constructed. Let the sets representing the number of people participating in the mathematics, physics, and chemistry groups be $A, B, C$, respectively. Then, card $(A \cap B \cap C)=0, \operatorname{card}(A \cap B)=6, \operatorname{card}(B \cap C)=4$.

Using the formula $\operatorname{card}(A \cup B \cup C)=\operatorname{card}(A)+\operatorname{card}(B)+$ $\operatorname{card}(C)-\operatorname{card}(A \cap B)-\operatorname{card}(A \cap C)-\operatorname{card}(B \cap C)+$ $\operatorname{card}(A \cap B \cap C)$,

we get $36=26+15+13-6-4-\operatorname{card}(A \cap C)$, so $\operatorname{card}(A \cap C)=8$. The answer should be 8.