Keeping the place of 6 fixed in 6350947, the smallest number by rearranging other digits is
6975430
6043579
6034579
6034759
We must keep the digit 6 exactly where it is, and only rearrange the other digits to make the whole number as small as possible.
Step 1: List the other digits: 3, 5, 0, 9, 4, 7.
Step 2: To get the smallest number, arrange these digits in increasing order (smallest first).
So we order them as: (0,;3,;4,;5,;7,;9).
Step 3: Put these digits after the fixed 6 in the same order. That gives:
(6;0;3;4;5;7;9)
Therefore the smallest number is 6034579, which is option C.