Unable to send ping from host A via B to C

Question

There is a network of three computer.

Problem: Host A (192.168.1.1) can send ping to host B (10.10.0.5, also 192.168.1.2), but can not to send C (10.10.0.6, 10.10.0.7).

Host A say: "10.10.0.6 = Destinantion Host Unreachable."

What I do wrong?

               route
+-----------+  dst 0.0.0.0     gw 192.168.1.2 eth0
|           |  dst 10.10.0.0   gw  0.0.0.0    eth0 
|           |  dst 192.168.1.0 gw 0.0.0.0     eth0
+-----------+
A:eth0 | 192.168.1.1
       |
B:eth0 | 192.168.1.2
+-----------+   route
|           | dst default     gw 10.10.0.6 eth1 
|           | dst 10.10.0.6   gw * eth1
|           | dst 10.10.0.7   gw * eth1
+-----------+ dst 192.168.1.0 gw * eth0
B:eth1 | 10.10.0.5
       |
C:eth0 | 10.10.0.6
+-----------+ route
|           | dst default     gw 10.10.0.7 eth1 
|           | dst 10.10.0.    gw *         eth1
|           | dst 192.168.1.0 gw *         eth0
+-----------+  
C:eth1 | 10.10.0.7
       |

Answer 1

Remove this route from A:

dst 10.10.0.0   gw  0.0.0.0    eth0 

It's preventing the machine from using the default route to get to the 10.10.x.x network.