Hi Yesim,
That post from MSE is very old. The "HiddenLayers" sub-option for Predict has been removed. In that example "HiddenLayers" -> {4, 3, 3} means 3 fully connected linear layers with output vector sizes of 4, 3, 3.
If you want complete control over the NN then I suggest not using Predict with Method -> "NeuralNetwork". Instead build the network using specific layers in NetChain and NetGraph and then NetTrain. Each layer type has parameters that can be controlled and there are a lot of customization options for NetTrain. You will have to study the documentation.
NetChain[{4, 3, 3}] (* Equivalent to "HiddenLayers" -> {4, 3, 3} *)
You have not provided any details about the problem you are trying to solve so it is hard to provide more specific advice.
