Let's define
x: gross income
26.2% of the gross income goes to pay taxes. That is, 0.262x
The gross income minus taxes make the take-home pay. Her take-home pay is $4,784.95, then
x - 0.262x = 4,784.95
0.738x = 4,784.95
x = 4,784.95/0.738
x = 6483.67
Her monthly gross income is $6,483.67
