Q6: Order plus degree of $\frac{d}{dx}\left[\left(\frac{dy}{dx}\right)^4\right] = 0$

As printed, the power 4 is written outside the square bracket. The bracket holds only $\frac{dy}{dx}$⁠, so it is the same as $\left(\frac{dy}{dx}\right)^4$⁠, and $\frac{d}{dx}$ acts on that power.

Watch out: do not read it as $\left(\frac{d^2y}{dx^2}\right)^4 = 0$⁠. That has order 2 and degree 4, so $m + n = 6$⁠, which is not an option.

Differentiate $\left(\frac{dy}{dx}\right)^4$ by the chain rule, with $u = \frac{dy}{dx}$⁠:

The derivative of $\frac{dy}{dx}$ is $\frac{d^2y}{dx^2}$⁠, which gives the line above.

The order is the order of the highest derivative present. The degree is the power of that highest derivative, once the equation is a polynomial in its derivatives, as it is here.

Watch out: the cube belongs to $\frac{dy}{dx}$⁠, which is not the highest derivative, so it does not set the degree.