What is the number of 6 digit numbers that can be formed only by...

Sum of digits $=0+1+2+3+4+5=15$ All numbers are divisible by 3. To make it divisible by 6 , it must be divisible by 2 i.e. even number at unit place. Case 1 : When 0 is at unit place
Number of numbers $=5!=120$ Case $2: 2,4$ at unit place
Number of numbers $=4!\times 4 \times 2=192$ Total numbers $=120+192=312$.