Answer
The man should apply a force of $517N$ to create an upward acceleration of $1.2m/s^2$.
Work Step by Step
The pulling force $P$ the man applies is changed into the tension $T$ in the rope, which pulls both the man and the platform.
There are 2 parts of the rope separated by the pulley, both have tension forces $T$ helping to pull the system up. So, $\sum T=2T$
Opposing the upward motion is the weight of the system. To create an upward acceleration of $1.2m/s^2$, $T$ has to be $$2T-mg=ma$$ $$2T=m(g+a)=94(9.8+1.2)=1034N$$ $$P=T=517N$$
