The resultant resistance of two resistance wires in series combination is 108 ohm and in parallel combination is 24 ohm. find the value of individual resistance.

Call the two resistors 'x' and 'y'.

In series, the resultant resistance is their sum: x + y = 108
Notice that y = 108 - x.  I think we'll use that very soon.

In parallel, the resultant resistance is (their product) / (their sum) = xy/108 = 24

Multiply each side by 108:

xy = 2,592

Substitute for 'y' :

x(108 - x) = 2,592

108x - x² = 2,592

-x² + 108x - 2,592 = 0

x² - 108x + 2,592 = 0

Use the quadratic formula to find:

x = 72 . . . then y = 108 - 72 = 36
or
x = 36 . . . then y = 108 - 36 = 72

The individual resistors are 36Ω  and  72Ω .