Negative consequentialism is a big word that means making decisions based on the bad things that can happen instead of the good things that can happen.
Here's an example: Let's say you're trying to decide whether to go outside and play in the park or stay inside and play video games all day. If you use negative consequentialism, you'll think about all the bad things that could happen if you go outside: you could get sunburned, you could get lost, you could fall down and hurt yourself, etc. If you use positive consequentialism, you'll think about all the good things that could happen if you go outside: you could have fun playing with your friends, you could enjoy the sunshine, you could get some exercise, etc.
So basically, negative consequentialism is about avoiding bad things, while positive consequentialism is about seeking out good things. Neither one is necessarily right or wrong, it just depends on what kind of person you are and what situation you're in.