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fan out is the number of gates one gate is driving i.e number of gates connected to the o/p of a gate. Like in this question for 2 fanout you connect 2 NOT gates at the o/p of the inverter. This will increase the load seen by the inverter and hence increases the propagation delay.
Same in the case of NAND you connect o/p of NAND gate to 2 (1-4) NAND gates and compare the results
do i need to connect capacitors after the nand gate to do the simulation?
no
it looks like a digital design example