First of all, the learning rate is indeed 0.9.

For delta(W14), from the formula on Slide #26,

• learning rate is 0.9
• y1 = 1 (output of node 1)
• f'4(X.W) = y4*(1-y4) = 0.332 * (1-0.332)
• W46 =-0.3
• Err6 = f'6(X.W)(y'6-y6) = y6*(1-y6)*(y'6-y6) = 0.474 * (1-0.474) * (1-0.474)

So delta(W14) = 0.9 * 1 * 0.332 * (1-0.332) * (-0.3) * 0.474 * (1-0.474) * (1-0.474) = -0.00785.

So the new W14 = 0.2 + (-0.00785) = 0.192

I probably missed the -0.3 in my calculation during class. Sorry about that.