The cart will be pulled to the right by the hanging mass, so by Newton's second law, the net force on the cart is
T - 25 N = (8 kg) a
where T is the tension in the rope and a is the acceleration.
The hanging mass has a net force of
(6 kg) g - T = (6 kg) a
where g = 9.8 m/s².
Adding these equations together eliminates T, and we can solve for a :
(T - 25 N) + ((6 kg) g - T ) = (14 kg) a
33.8 N = (14 kg) a
a = (33.8 N) / (14 kg) ≈ 2.4 m/s²
Then the tension in the rope is
T - 25 N = (8 kg) (2.4 m/s²)
T ≈ 25 N + 19.31 N ≈ 44 N