【Answer】 4
【Analysis】 Number puzzle, breakthrough, multiplication and division. There are 3 different numbers from 1 to 8 in the multiplication: $2 \times 3=6, 2 \times 4=8$. The numbers not involved are $1, 5, 7$. 2 can only be filled in the lower left corner or the upper right corner, with adjacent sides forming a multiplication equation and a division equation. In fact, there are 4 ways to fill, all of which are derived from the same filling method through symmetric exchange.
3. Put the operation symbols " +", " -", " ×", and " ÷" into the four positions in the figure, and fill the numbers " $1, 2, 3, 4, 5, 6, 7, 8$ " into the eight blank spaces in the figure, so that the four equations formed by the quadrilateral all hold true. How many ways are there to do this?