I agree with 6/23
I did it with a probability tree.
Say you chose a red wood triangle
there are 2*3*4 = 24 blocks, you chose one and there are 23 blocks left
12 of those are NOT wood
Of the 12 that are not wood, 2/3 of them are not red, that is 8 are not red or made of wood
Of these 8, 3/4 of them are not a triangle so that is 8*3/4 = 6 are not made of wood, or red or a triangle
So that is 6/23 will not share any of the same traits.
If you draw a probability tree it might be easier for you to see.