(C) $\left \{ wxyw|w,x,y \in (a+b)^{+} \right \}$ is NOT regular
But, (A) and (B) are regular.
regex for $\left \{ wxwy|w,x,y \in (a+b)^{+} \right \} = \left ( a(a+b)^{+}a + b(a+b)^{+}b \right )(a+b)^{+}$
and regex for $\left \{ xwyw|w,x,y \in (a+b)^{+} \right \} = (a+b)^{+} \left ( a(a+b)^{+}a + b(a+b)^{+}b \right )$
NOTE : put the minimal strings in w first and you get two regex $R_1$ and $R_2$. Then for next higher strings of w try to build (1) (Or, (2) ) using those $R_1$ , $R_2$. If it is possible to derive all the next strings of L = $\left \{ wxwy \right \}$ only using $R_1$ and $R_2$, then $R_1 + R_2$ is the net regular expression for L.