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The given word has 8 letters; they all are different.
If four-letter word contains letter Q, it can occupy any of 4 positions of the 4-letter word, giving you 4 primary options.
For the rest 3 positions, you have 7*6*5 = 210 choices, that are secondary options.
The full number of combinations under the question is then 4*210 = 840. ANSWER
Solved.
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From the context, I understand the meaning of this question in THIS way :
How many different four-letter words can be formed of the letters of the word EQUATION containing letter Q?
@greenestamps interprets the problem differently. So he got different solution and different answer.
Since your formulation admits different interpretations, it is FAR from to be perfect.