I am taking $x=r\cos\phi, y=r \sin\phi$
$ dx=-r \sin\phi d\phi+\cos\phi dr, dy=r\cos\phi d\phi + \sin\phi dr$
it is working with jacobian of$(x,y) $concerning $(u,v)$ and cross product i.e. if we take $|dx × dy|$ but if I am directly multiplying $dxdy$ then I am getting the wrong answer I want to know the reason behind what's happening in the background of these equations why directly $dxdy$ gives the wrong result.
When you write $\iint dxdy$, it isn't correct to interpret $dxdy$ as a product of two things - it's an instruction to integrate with respect to each of $x$ and $y$ in turn. When you are changing variables, you are asking how to integrate instead with respect to each of $r$ and $\theta$ in turn, and it turns out that this requires the introduction of the Jacobian factor $$\left| \begin{array} {cc} \frac{\partial x}{\partial r} & \frac{\partial x}{\partial \theta} \\ \frac{\partial y}{\partial r} & \frac{\partial y}{\partial \theta} \end{array}\right|.$$ In general (e.g. in the three-variable case), this is a determinant rather than a cross product, though a 'cross product' calculation gives the same result with two variables. An intuitive answer to why the Jacobian is necessary is that, if you think of $dxdy$ and $drd\theta$ as alternative 'elements of area' the Jacobian is the determinant of the matrix which maps one to the other - hence the area scale factor.