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Let the mass of the object be $m$.
Given:
Initial velocity, $u = 0$
Applied force, $F = 15\text{ N}$
Time during which force acts, $t_1 = 4\text{ s}$

After the force ceases to act, the object moves with a constant velocity $v$.
Distance covered with uniform velocity, $s = 54\text{ m}$
Time taken, $t_2 = 9\text{ s}$

Uniform velocity, $v = \frac{s}{t_2} = \frac{54}{9} = 6\text{ m/s}$

Acceleration during the first 4 seconds:
$v = u + a t_1$
$6 = 0 + a \times 4$
$a = \frac{6}{4} = 1.5\text{ m/s}^2$

From Newton's second law:
$F = ma$
$m = \frac{F}{a} = \frac{15}{1.5} = 10\text{ kg}$

Ans: 10 kg