For the first layer of your circuit, compute the tensor product between the unitary matrix of the (swapped) CNOT gate and the identity matrix (using numpy's kron()). Do a similar operation for the second layer. You will obtain two 8x8 matrices. Then multiply them using numpy's matmul().
Here you have the working code:
import numpy as np
swapcnot = np.array([[1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [0, 1, 0, 0]])
layer1 = np.kron(np.eye(2),swapcnot )
layer2 = np.kron( swapcnot, np.eye(2) )
print( np.matmul(layer2,layer1) )
Output:
[[1. 0. 0. 0. 0. 0. 0. 0.]
[0. 0. 0. 1. 0. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 1. 0.]
[0. 0. 0. 0. 0. 1. 0. 0.]
[0. 0. 0. 0. 1. 0. 0. 0.]
[0. 0. 0. 0. 0. 0. 0. 1.]
[0. 0. 1. 0. 0. 0. 0. 0.]
[0. 1. 0. 0. 0. 0. 0. 0.]]