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Answer: $0$

$$\frac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O$$
letters used: $E, I, G, H, T, F, O, U, R, W$    total 10 letters

So digit $0$ must be used

$\therefore \dfrac{E\times I\times G\times H\times T } {F\times O\times U\times R }= T\times W\times O = 0$

$T$ appears on both sides so $T=0$

Hence the product $T\times  H\times R \times E \times E =0$.
 
 
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.