To solve the inequality -x² + 4x - 6 < 0, we can follow these steps:

1. Set the inequality equal to zero: -x² + 4x - 6 = 0.

2. Factor the quadratic equation: (x - 2)(-x + 3) = 0.

3. Set each factor equal to zero and solve for x:
x - 2 = 0 --> x = 2
-x + 3 = 0 --> x = 3

4. Plot these values on a number line:
-∞ 2 3 +∞

5. Choose a test point in each interval and plug it into the original inequality to determine if it is true or false.

Test x = 0: -0² + 4(0) - 6 < 0 --> -6 < 0 (True)
Test x = 2.5: -2.5² + 4(2.5) - 6 < 0 --> -1.25 < 0 (True)
Test x = 4: -4² + 4(4) - 6 < 0 --> 2 < 0 (False)

6. Based on the test points, we can see that the inequality is true for x < 2 and 2 < x < 3.

Therefore, the solution to the inequality -x² + 4x - 6 < 0 is 2 < x < 3.