Counting the number of layers in a neural network
This is a 2-layer network because it has a single hidden layer and an output layer. We don't count the first layer. When we say 3 layers, we actually mean 2 hidden layers and an output layer. Perhaps this helps you?

EDIT: We don't count the input layer because there's no parameter (bias + weights). In actual implementation, it's not implemented. Netural network framework simply "connects" the input features to the first adjustable layer (eg: hidden layer).