First, you can't rewire your 2x12 speaker cab as a 16 ohm cab. The speakers inside that cab are each 16 ohms and are wired in parallel. Now for the explanation.
Wiring speakers in series - to calculate the effective resistance, you add the resistances of each of the speakers wired in series.
Let's use your 2x12 cab as an example, each of the two speakers having a resistance of 16 ohms. If wired in series, the effective resistance of the cab is 16 + 16 = 32 ohms.
For a series configuration, you take a wire from the tip of the input jack on your cab and connect it to the + side of the first speaker. You connect the - side of the first speaker with the + side of the second speaker with a second wire. Finally, you connect the - side of the second speaker to the sleeve of the input jack with a third wire.
Wiring speakers in parallel - to calculate the effective resistance, you use the following sequence of calculations:
Step one: For each of the speakers in parallel, calculate the reciprocal of the resistance (1/R). For a 16 ohm speaker, the reciprocal is 1/16 or 0.0625.
Step two: Add each of the reciprocals from step one. For our example, we have 2 speakers, so the answer is 0.0625 + 0.0625 = 0.125.
Step three: Take the reciprocal of the answer from step two. For our example, 1/0.125 = 8.
So, for two 16 ohm speakers wired in parallel, the effective resistance is 8 ohms.
For a parallel configuration, you take a wire from the tip of the input jack on your cab and connect it to the + side of the first speaker. You connect the + side of the first speaker with the + side of the second speaker with a second wire. You connect the - side of the first speaker with the - side of the second speaker with a third wire. Finally, you connect the - side of the second speaker to the sleeve of the input jack with a fourth wire.
As a final example, let's take your 2x12 cab and wire it in parallel with your single 16 ohm speaker. The 2x12 cab has an effective resistance of 8 ohms, so we have an 8 ohm resistance and a 16 ohm resistance in parallel.
Step one: Reciprocals are 1/8 = 0.125 and 1/16 = 0.0625
Step two: Sum of reciprocals is 0.125 + 0.0625 = 0.1875
Step three: Reciprocal of result is 1/0.1875 = 5.333...
So the answer is a little over 5 ohms.
If you were to wire your 2x12 cab and your single 16 ohm speaker is series, the effective resistance would be 8 + 16 = 24 ohms.
End of Ohms Law 101