Balancing a redox equation involves ensuring that the number of atoms of each element and the total charge are the same on both sides of the equation. To balance the redox equation for the reaction between P4, NaOH, and H2O2 in a basic medium, we need to follow the steps below:

1. Identify the oxidation states of each element in the reaction:
P4: The oxidation state of phosphorus in P4 is 0.
NaOH: Sodium (Na) has an oxidation state of +1, oxygen (O) has an oxidation state of -2, and hydrogen (H) has an oxidation state of +1.
H2O2: Oxygen (O) has an oxidation state of -1, and hydrogen (H) has an oxidation state of +1.

2. Determine the changes in oxidation states for each element:
P4: The oxidation state of phosphorus changes from 0 to -3 in the product PH3 and from 0 to +1 in the product H2PO2-.
NaOH: The oxidation state of sodium remains unchanged at +1, while the oxidation state of oxygen changes from -2 to -1.
H2O2: The oxidation state of oxygen changes from -1 to -2, and the oxidation state of hydrogen remains unchanged at +1.

3. Write the unbalanced half-reactions:
Oxidation half-reaction: P4 -> PH3
Reduction half-reaction: H2O2 -> H2PO2-

4. Balance the changes in oxidation states by adding water molecules and hydroxide ions (OH-) as necessary to the half-reactions:
Oxidation half-reaction: P4 + 6H2O -> 4PH3 + 12e-
Reduction half-reaction: 4H2O2 + 12e- -> 4H2PO2-

5. Balance the number of electrons transferred by multiplying the half-reactions:
Oxidation half-reaction: 4P4 + 24H2O -> 16PH3 + 48e-
Reduction half-reaction: 16H2O2 + 48e- -> 16H2PO2-

6. Balance the number of atoms of each element by adding appropriate coefficients:
Oxidation half-reaction: 2P4 + 12H2O -> 8PH3 + 24e-
Reduction half-reaction: 8H2O2 + 24e- -> 8H2PO2-

7. Combine the balanced half-reactions and cancel out the electrons:
2P4 + 12H2O + 8H2O2 -> 8PH3 + 8H2PO2-

8. Simplify the equation by dividing through by the smallest whole-number coefficient:
P4 + 6H2O + 4H2O2 -> 4PH3 + 4H2PO2-

Thus, the balanced redox equation for the reaction between P4, NaOH, and H2O2 in a basic medium is option 'D': 2P4 + 16OH- + 8H2O2 -> 8PH3 + 8H2PO2-.