The total number of six digit natural number that can be made with 1, 2, 3, 4 if all digits are to appear in the same number at least once.

Type (1) any one digits of 1, 2, 3, 4  and remaining digits only ones

1, 2, 3, 4, 44……..etc

No of digits ${=}^4{\mathrm{C}}_1\times \frac{6!}{3!}=480$

Type (2) Any two digits of 1, 2,3, 4 appears twice and reaming only once

i,e 1, 2, 33, 44 ……etc 

no of digits ${=}^4{C}_2\times \frac{6!}{2!2!}=1080$

total  = 480 + 1080 = 1560