4. A two-digit number was increased by 3, and it turned out that the sum is divisible by 3. When 7 was added to this same two-digit number, the resulting sum was divisible by 7. If 4 is subtracted from this two-digit number, the resulting difference is divisible by four. Find this two-digit number.
4. Since the sum of a two-digit number and three is divisible by three and the second addend is also divisible by three, the unknown two-digit number is divisible by three. Similarly, we can establish that the two-digit number is also divisible by seven and four. Thus, it is divisible by $84(3 \times 4 \times 7=84)$. Among the two-digit numbers divisible by eighty-four, there is only one - 84.

Answer: 84.