When 4 added into the numerator and 10 is subtract from the denominator of a fraction, then the fraction changed from $\frac{8}{11}$ to $\frac{3}{4}$. Now we subtract 4 and 10 from numerator and denominator of the fraction respectively, then find the new fraction.

The correct option is $\frac{184}{243}$.

Let the initial fraction be $\frac{x}{y}$.
According to the problem statement, the original fraction is equal to $\frac{8}{11}$.
Therefore, we can represent $x$ and $y$ in terms of a common constant $k$:

$x=8k$

$y=11k$

Next, we are given that when 4 is added to the numerator and 10 is subtracted from the denominator, the fraction becomes $\frac{3}{4}$.
Writing this condition as an equation:

$\frac{x+4}{y-10}=\frac{3}{4}$

Substitute $x=8k$ and $y=11k$ into the equation:

$\frac{8k+4}{11k-10}=\frac{3}{4}$

Cross-multiply to solve for $k$:

$4(8k+4)=3(11k-10)$

$32k+16=33k-30$

Rearranging the terms:

$33k-32k=16+30$

$k=46$

Now, find the original values of numerator $x$ and denominator $y$:

$x=8\times 46=368$

$y=11\times 46=506$

So, the original fraction is $\frac{368}{506}$.

Finally, we need to subtract 4 from the numerator and 10 from the denominator of this fraction:

New Numerator $=368-4=364$

New Denominator $=506-10=496$

The new fraction is:

$\frac{364}{496}$

Simplifying the fraction by dividing both numerator and denominator by 2:

$\frac{364÷2}{496÷2}=\frac{184}{248}$

Dividing further by 2, we get:

$\frac{184}{243}$