Calculate the determinant of the given matrix.

The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is given by $ad - bc$.
For the given matrix $\begin{bmatrix} y-1 & 2 \\ 4 & 3 \end{bmatrix}$, the determinant is:

$$(y-1)(3) - (2)(4)$$

$$3y - 3 - 8 = 4$$ $$3y - 11 = 4$$

Add 11 to both sides of the equation:

$$3y = 4 + 11$$ $$3y = 15$$

Divide by 3:

$$y = \frac{15}{3}$$ $$y = 5$$

The value of $y$ is:

$$5$$