The Boolean expression $AB+A\overline{B}+\overline{A}C+AC$ is unaffected by the value of the Boolean variable $...............$

$AB+A\overline{B}+\overline{A}C+AC$

Take $A$ common from first two terms:

$A(B+\overline{B})+\overline{A}C+AC$

Since,

$B+\overline{B}=1$

So,

$A(1)+\overline{A}C+AC$

$=A+\overline{A}C+AC$

Now,

$A+AC=A$

So,

$A+\overline{A}C$

Using identity $A+\overline{A}C=A+C$

Therefore, the simplified expression is:

$A+C$

The final expression does not contain $B$, so it is unaffected by the value of $B$.