The number of words, with or without meaning, that can be formed by...

From the given word, $S - 2, L - 2, A, B, Y, U$.

Number of alike letter pairs $= 2$

Number of ways to select one pair$= C1 2$

Number of distinct letters$= 5$

Number of ways to select two distinct letters$= C2 5$

Number of ways to arrange four letters if two are alike$= \dfrac{4 !}{2 !}$

Required number of ways $= C1 2 C2 5 \cdot \dfrac{4 !}{2 !} = 2 \cdot 10 \cdot \dfrac{24}{2} = 240$