Taking into account the statement above: "Explain in your own words how the thesis of causal determinism would seem at odds with the possibility of a person's doing something of his or her own free will. (This will involve explaining what causal determinism is (how it differs from fatalism) and what free will involves, and why the truth of the one would seem to conflict with the possibility of the other.)"
the causes of the event are sufficient to occur in which no other event would occur.
For example: light a match
For the fatalism, the action is to predetermine with no causal antecedents for the action to occur.
Free will involves the condition that you would do otherwise if you had chosen.
And the issue of where they conflict is that you cannot both be determined and free.
For example: the Bridge Breaking.
Hope this helps.