If a meaningful four-letter word can be formed from the $4^{\text{th}}$, $5^{\text{th}}$, $7^{\text{th}}$, and $8^{\text{th}}$ letters of the word 'RECONCILE', how many meaningful words can be formed using these letters exactly once?

Let's extract the specified letters from the word 'RECONCILE':
* $1^{\text{st}}$ letter = R
* $2^{\text{nd}}$ letter = E
* $3^{\text{rd}}$ letter = C
* $4^{\text{th}}$ letter = O
* $5^{\text{th}}$ letter = N
* $6^{\text{th}}$ letter = C
* $7^{\text{th}}$ letter = I
* $8^{\text{th}}$ letter = L
* $9^{\text{th}}$ letter = E

The extracted letters are: O, N, I, L

Now, let's form meaningful English words using all four letters exactly once:

1. LION (a large wild cat)
2. LOIN (the part of the body on both sides of the spine between the lowest ribs and the hipbones)

No other standard, common meaningful English words can be formed using these four letters.

Therefore, exactly two meaningful words can be formed.