6. As shown in Figure 1, an ant starts from the center point $A$, walks five steps and returns to $A$, without returning to $A$ in between. The number of different ways to do this is $\qquad$ (At each step, the ant can only move to an adjacent point, and it is allowed to walk on the same route more than once).
6. 180 .

Starting from point $A$, there are two directions: along point $B$ or $C$.
(1) If moving along point $B$, the next steps are along point $C$, $D$, or $E$. This means two steps have already been taken, and there are three steps left. From point $C$, there are 8 ways to return to point $A$ in three steps, from point $D$ there are 5 ways, and from point $E$ there are 6 ways. In total, there are $8 \times 2 + 5 \times 2 + 6 = 32$ ways.
(2) If moving along point $C$, the next steps are along point $B$ or $D$. From point $B$, there are 9 ways to return to point $A$ in three steps, and from point $D$ there are 5 ways. In total, there are $9 \times 2 + 5 \times 2 = 28$ ways.
In summary, there are $(28 + 32) \times 3 = 180$ ways.