Arrange the ions:

Cu^2+, Ni^2+, Mg^2+, & Zn^2+
in order of decreasing ability to be reduced...

& in order of decreasing ability to be oxidized

Look up the reduction potentials.

Most negative is easiest to reduce.
Most positive is easiest to oxidize.

To arrange the ions in order of decreasing ability to be reduced, we need to consider their reduction potentials. The greater the reduction potential, the stronger the oxidizing agent and the greater the ability to be reduced.

Step 1: Look up the standard reduction potentials for each ion.
The standard reduction potentials (E°) can be found in reference sources like textbooks or online databases. Here are the standard reduction potentials for the given ions:

Cu^2+: +0.34 V
Ni^2+: -0.23 V
Mg^2+: -2.37 V
Zn^2+: -0.76 V

Step 2: Arrange the ions in decreasing order of their reduction potentials.
Starting with the ion that has the highest reduction potential and moving to the one with the lowest, we obtain:

Mg^2+ > Zn^2+ > Ni^2+ > Cu^2+

Therefore, the ions arranged in decreasing ability to be reduced are: Mg^2+ > Zn^2+ > Ni^2+ > Cu^2+.

Now, let's arrange the ions in order of decreasing ability to be oxidized.

Step 1: Recall that the ability to be oxidized is the reverse of the ability to be reduced. Therefore, we can simply reverse the order from the previous step.

Cu^2+ > Ni^2+ > Zn^2+ > Mg^2+

So, the ions arranged in decreasing ability to be oxidized are: Cu^2+ > Ni^2+ > Zn^2+ > Mg^2+.