To determine the multiplicity of the factor \((x - 4)\) in the polynomial \(m(x)\), we need to consider the behavior of the graph at \(x = 4\):
- If \((x - 4)\) has an even multiplicity, the graph will touch the x-axis at \(x = 4\) and turn back without crossing it.
- If \((x - 4)\) has an odd multiplicity, the graph will cross the x-axis at \(x = 4\).
Given the described behavior of the graph \(m(x)\) where it starts in quadrant 2 (above the x-axis), descends to the x-axis and then rises again (implying the graph passes through the x-axis), the factor \((x - 4)\) must have odd multiplicity, because the graph crosses the x-axis at this point.
Thus, the multiplicity of \((x - 4)\) is described by Option #2: odd.