Decide what values of the variable cannot possibly be solutions for the equation. \[ \frac{1}{x-4}+\frac{1}{x+6}=10 \]

Step 1 ：Decide what values of the variable cannot possibly be solutions for the equation \(\frac{1}{x-4}+\frac{1}{x+6}=10\).

Step 2 ：The values of the variable that cannot possibly be solutions for the equation are the values that make the denominator of the fractions equal to zero. This is because division by zero is undefined in mathematics.

Step 3 ：Therefore, we need to find the values of x that make x-4=0 and x+6=0.

Step 4 ：The values of the variable that cannot possibly be solutions for the equation are \(\boxed{4}\) and \(\boxed{-6}\).