6. Fill the numbers $1 \sim 9$ into a $3 \times 3$ grid such that each cell contains a unique number. Two cells with a common edge are called a "number pair." Determine the maximum number of number pairs, where one number in the pair is a multiple of the other.
6. Notice that 1 is a divisor of $1 \sim 9$.

Therefore, 1 is placed in the center of the grid. To maximize the number of pairs where one number is a multiple of the other, it is observed that 2 and 3 should be placed in the four corners of the grid.
Figure 2 shows one such arrangement, in which the pairs $(2,6),(6,3)$, $(2,8),(8,1),(1,9)$, $(6,1),(8,4),(1,5)$, $(3,9)$, a total of 9 pairs, satisfy the condition.