To determine what number Rahul can multiply the equation \( y = \frac{23}{6}x + 14 \) by to eliminate any fractions, we should first rewrite the equation in a form that clearly shows any fractions.
The given equation is: \[ y = 23x + 14 \]
However, this appears to be a miscommunication regarding fractions. It seems you might mean to consider a version where \( 23x \) is expressed with a fraction. For example, if it was in the form: \[ y = \frac{23}{6}x + 14 \]
In that case, multiplying through by \( 6 \) would clear the fraction: \[ 6y = 23x + 84 \]
So to eliminate fractions in the form of \( \frac{23}{6} \), Rahul can multiply the equation by \( 6 \).
If your original equation is actually \( y = 23x + 14 \) with no fraction involved, then he's already in the standard form, and no multiplication is necessary.
However, considering the context and frequent need to clear fractions, \( 6 \) may be the intended response.
Thus, from the options provided, the number by which he can multiply the equation in order to clear the fractions and rewrite it in standard form would be: 6