6. (5 points) If three times a two-digit number minus 4 is a multiple of 10, and four times the number minus 15 is greater than 60 and less than 100, then the two-digit number is $\qquad$ .
【Analysis】Obviously, the difference between three times a two-digit number and 4 is a multiple of 10, which means the unit digit of the number obtained by tripling this two-digit number is 4. The unit digit of a two-digit number that, when multiplied by 3, results in a number with a unit digit of 4 is 8. Given that the difference between four times this number and 15 is greater than 60 and less than 100, we can determine the range of this two-digit number, making it easy to find the number.

【Solution】According to the analysis, the difference between three times a two-digit number and 4 is a multiple of 10, which means the unit digit of the number obtained by tripling this two-digit number is 4,

and the unit digit of a two-digit number that, when multiplied by 3, results in a number with a unit digit of 4 is 8;
Given that the difference between four times this number and 15 is greater than 60 and less than 100, we can determine the range of this two-digit number:
$$
\text { Greater than: } \frac{60+15}{4}=18 \frac{3}{4} \text {, Less than: } \frac{100+15}{4}=28 \frac{3}{4} \text {, }
$$

In summary, this two-digit number is: 28.
Therefore, the answer is: 28.