To solve the inequality \((x - 3)(x - 4) \leq 0\), we can use the concept of intervals and critical points.

1. Find the critical points by setting each factor to zero:
  \(x - 3 = 0 \Rightarrow x = 3\)
  \(x - 4 = 0 \Rightarrow x = 4\)

2. Create intervals using the critical points: \(x < 3\), \(3 < x < 4\), and \(x > 4\).

3. Test a point within each interval to determine the sign of the expression \((x - 3)(x - 4)\):
  - For \(x = 2\), \((2 - 3)(2 - 4) = 2 > 0\)
  - For \(x = 3.5\), \((3.5 - 3)(3.5 - 4) = -0.25 < 0\)
  - For \(x = 5\), \((5 - 3)(5 - 4) = 2 > 0\)

Based on the signs, the solution intervals are:
- For \((x - 3)(x - 4) \leq 0\), the solution is \(3 \leq x \leq 4\).