Step 1: Split the plate into two parts.
The plate has $6$ slots: the first two must be distinct digits, and the last four must be distinct capital letters. We count each part and multiply.
Step 2: Fill the first digit slot.
There are $10$ digits ($0$ through $9$), so the first digit can be chosen in $10$ ways.
Step 3: Fill the second digit slot.
It must differ from the first, so $9$ choices remain. The two digits together give $10\times9=90$ ways.
Step 4: Fill the four letter slots.
The letters must all be different. The first letter has $26$ choices, the next $25$, then $24$, then $23$.
Step 5: Multiply the letter choices.
$26\times25\times24\times23=358800$.
Step 6: Combine both parts.
Total plates $=90\times358800=32292000$. \[ \boxed{32292000} \]