in the future you might want to reconsider your "Ready fire Aim" method of buying PC upgrades and research/ask BEFORE buying something.................sorry but your might be out of luck in this case as both supplies are either non ATX in size and Pinout
your video card appears to require AUX power (IE- has a power connector on the card)
the HP 6300 Pro is available in two form factors "SFF" = small form factor that only takes low profile cards and has a 240 watt power supply and a mini tower that takes full height cards with a power supply of 320 watts that DOES NOT support/have GPU power connectors, as such any video card installed must be under 75 watts (HP says 35 watts for the tower 6300)
your only hope is that you have a minitower 6300 pro case, as this one uses a ATX sized supply with non atx power leads to the motherboard however several sellers do sell a adapter to allow you to replace the hp minitower supply with a standard ATX supply that has the necessary GPU power connectors
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