103 Using the digits $1,2,3,4$ to form a 6-digit number, each digit must be used at least once, the number of 6-digit numbers that can be formed is $\qquad$.

Translating the text into English while preserving the original formatting and line breaks, the result is as follows:

103 Using the digits $1,2,3,4$ to form a 6-digit number, each digit must be used at least once, the number of 6-digit numbers that can be formed is $\qquad$.
1031560 . If one digit is used 3 times, such as 1, then in 6 positions, choose 3 positions to place 1, there are $C_{6}^{3}$ ways, and the remaining 3 positions to place $2,3,4$, there are 3! ways, in total
$$
C_{4}^{1} \cdot C_{6}^{3} \cdot 3!=480 \text { (numbers). }
$$

If 2 digits are used 2 times each, such as 2 ones and 2 twos. In 6 positions, choose 2 to place 1, there are $C_{6}^{2}$ ways, then in the remaining 4 positions, choose 2 to place 2, there are $C_{4}^{2}$ ways, and finally place $3, 4$ in 2! ways, so in total there are
$$
C_{4}^{2} \cdot C_{6}^{2} \cdot C_{4}^{2} \cdot 2!=1080 \text { (numbers). }
$$

In summary, there are
$$
480+1080=1560 \text { (numbers). }
$$