Wire you confused?

This may be somewhat complex but let's approach it in a simpler way. I'm going to place points on the circuit to define certain positions:

Figure 1

since the green wire is nothing but a connection between points C and D, we can change the location of the Terminal of the 3 ohm on point D to any place on the green wire:

Figure 2

now it is obvious:

6 parallel to 3 = 2ohms

7 in series with 2 = 9 ohms

9 in parallel with 9 = 4.5 ohms

4.5 in series with 8 = 12.5 ohms

It could be more confused if you had replaced the 7ohm resistor with a wire :) .

The 6 ohm resistor is cancelled...7&3 resistors are series R=10 ohm..10&9 are parallel R=4.7 THEN 8&4.7 resistors are series R total is 12.7 ohm