<s>[INST] When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$... When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction?
I tried,
Let the numerator of the fraction be $x$ and the denominator be $y$.
Accordingly, $$\frac{x+4}y=\frac xy+\frac 23$$
I am not able to find the second equation. 
 [/INST] In general you are correct: to solve for two unknowns, you would usually need two equations.  But in this case you are lucky, and the one equation gives a solution for the one unknown you are asked to find.
$\dfrac{x+4}{y}=\dfrac{x}{y}+\dfrac{2}{3}$ so multiplying both sides by $3y$ gives $3x+12 = 3x+2y$ making the denominator $y=6$.
It gives no specific solution for $x$, for example: $\dfrac{5+4}{6}=\dfrac{5}{6}+\dfrac{2}{3}$ and $\dfrac{7+4}{6}=\dfrac{7}{6}+\dfrac{2}{3}$. 
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