When a force F is applied on a spring with a spring constant k Hooke's law gives the extent by which the spring is compressed as x where F = k*x or x = F/k.
If two springs are connected in series and a force F applied on them, the force applied is the same for both the springs. The resulting change in length varies.
In the problem, the two spring connected in series have a spring constant of 280 N/m and 340 N/m. When a force of 24 N is applied on the system each is compressed by a different length that is inversely proportional to its spring constant. The spring with a spring constant 280 N/m is compressed by 24/280 = 0.08571 m and the other spring with a spring constant 340 N/m is compressed by 24/340 = 0.0705 m.