Treat "QU" as a single unit. The letters to arrange are now QU, E, E, giving us 3 units (QU, E, E) to permute, which yields $\frac{3!}{2!} = 3$ arrangements for the letters, and each arrangement can occur in 2 ways because of the distinct positions of E's (the two indistinguishable E's). Thus, the total is $3 \times 2 = 12$.