The probability of choosing a plum from Jameel's box is \(\frac{5}{8}\) because there are 5 plums out of a total of 8 fruits.

The probability of choosing a plum from Rosa's box is \(\frac{x}{x+6}\) because there are x plums out of a total of \(x + 6\) fruits.

The probability that both fruits chosen are plums is given by:

\(\frac{5}{8} \times \frac{x}{x+6} = \frac{1}{4}\)

To solve for x, multiply both sides by \(8(x+6)\):

\(5x = 2(x+6)\)

Expand and simplify:

\(5x = 2x + 12\)

Subtract \(2x\) from both sides:

\(3x = 12\)

Divide both sides by 3:

\(x = 4\)