1. Identify the concept

   For actinoids, the highest oxidation state generally increases up to the middle of the series and then decreases. We need the highest possible oxidation states of:

   • Uranium $(U)$
   • Plutonium $(Pu)$

2. Electronic considerations

   Actinoids can show variable oxidation states because electrons from $5f$, $6d$, and $7s$ orbitals can participate in bonding.

3. Known highest oxidation states

   • Uranium commonly shows oxidation states $+3, +4, +5, +6$. Its highest stable oxidation state is $+6$.
   • Plutonium shows oxidation states $+3, +4, +5, +6$, and it can also attain $+7$ under strongly oxidizing conditions. So its highest possible oxidation state is $+7$.

4. Match with the options

   • A: $4$ and $6$ ❌
   • B: $6$ and $4$ ❌
   • C: $7$ and $6$ ❌
   • D: $6$ and $7$ ✅

5. Final answer

   The highest possible oxidation states of uranium and plutonium are: $+6 \text{ and } +7$ respectively.

Therefore, the correct option is D.