How does tensor product/multiplication work in TensorFlow? In Tensorflow, I saw the following example:

import tensorflow as tf 
import numpy as np 

mat_a = tf.constant(np.arange(1,13, dtype=np.int32), shape=[2,2,3])  
mat_b = tf.constant(np.arange(12,24, dtype=np.int32), shape=[2,3,2])  
mul_c = tf.matmul(mat_a, mat_b)

with tf.Session() as sess:  
   runop = sess.run(mul_c)  
   print(runop) 

[[[ 88  94]  
  [214 229]]  
 [[484 508]  
  [642 674]]]


How does the tensor multiplication work?
You may want to read the documentation.

output[..., i, j] = sum_k (a[..., i, k] * b[..., k, j]), for all indices i, j.

For instance, in your example 

$~~88=1\times12+2\times14+3\times16,~~~94=1\times13+2\times15+3\times17$
$214=4\times12+5\times14+6\times16,~229=4\times13+5\times15+6\times17$