Without solving the equations, which absolute value equation has no solution? A. $-|8 x-7|-1=6$ B. $|x-7|=0$ C. $-|3 x+5|=-8$ D. $|9-6 x|+4=12$

Step 1 ：Analyze each equation to determine if it has a solution or not.

Step 2 ：A. $-|8 x-7|-1=6$ has no solution because the left side will always be less than or equal to -1, while the right side is 6.

Step 3 ：B. $|x-7|=0$ has a solution (x = 7) because the absolute value can be zero if the expression inside is zero.

Step 4 ：C. $-|3 x+5|=-8$ has a solution because the left side will always be less than or equal to 0, and the right side is -8.

Step 5 ：D. $|9-6 x|+4=12$ has a solution because the left side will always be greater than or equal to 4, and the right side is 12.

Step 6 ：\boxed{\text{Final Answer: A. } -|8 x-7|-1=6}