Design a 100 watt inverter, but why when the circuit is connected to the power supply sparks out?
This inverter circuit consists of a 150 Watt boost converter to
increase the DC voltage of the solar panel to 24 Volts.


From what I can see, with a 24 volts DC supply, Q3 and Q4 will see about 24 volts on their gates with respect to ground. This is significantly beyond the stated absolute maximum rating in the data sheet extract above.
I'm not ruling out other things (should those MOSFETs survive the first few seconds) such as: -

MOSFET Shoot-through due to both MOSFETs on one side of the bridge simultaneously conducting as the (slow) gate drive switches.
1N4004 reverse recovery shoot-through (circa 30 us potentially)