Write the condition for constructive interference in terms of path and phase difference.

For constructive interference, the waves must arrive at a point in phase.
$1$. Phase difference $(\phi)$: The phase difference between the two interfering waves must be an integral multiple of $2\pi$. Mathematically, $\phi = 2n\pi$, where $n = 0, 1, 2, 3, ...$
$2$. Path difference $(\Delta x)$: Since the relation between path difference and phase difference is $\phi = \frac{2\pi}{\lambda} \Delta x$, substituting $\phi = 2n\pi$ gives $2n\pi = \frac{2\pi}{\lambda} \Delta x$. Thus, the path difference must be an integral multiple of the wavelength, $\Delta x = n\lambda$, where $n = 0, 1, 2, 3, ...$