4. (3 points) There are two two-digit numbers, A and B. $\frac{2}{7}$ of A equals $\frac{2}{3}$ of B. What is the maximum difference between these two two-digit integers? $\qquad$
【Solution】Solution: Let the first number be $a$, and the second number be $b$. According to the problem, we can set up the equation:
$$
\frac{2}{7} a=\frac{2}{3} b \text {, }
$$

Based on the fundamental property of ratios, we get: $a: b=\frac{2}{3}: \frac{2}{7}=7: 3$. Since both numbers are two-digit numbers, $100 \div 7=14 \cdots 2$, the largest share is 14, so the two numbers that meet the conditions are: $14 \times 7=98,14 \times 3=42$, $98-42=56$,

Answer: The maximum difference between these two two-digit numbers is 56.
Therefore, the answer is: 56 .