Explanation:
the perimeter of a rectangle is
2×length + 2×width
"simplified" means that we calculate everything "away" we can calculate and end up with the minimum of an expression around the variable (in our case p).
18p⁴ - 4p = 2×(6p⁴ - p) + 2×width
the first simplification is that we can divide everything by 2
9p⁴ - 2p = 6p⁴ - p + width
3p⁴ - 2p = -p + width
3p⁴ - p = width