the way that (someone) has handled (something)
To "handle" a situation means to deal with it. "The way that (someone) has handled" a situation means the things that they have done in response to that situation. For example, if one of your employees has done a bad job on a project, you can say:
I'm really not happy with the way that you've handled this.
This means "I'm not happy with the things that you did about this situation."
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