How do I apply the Nyquist criterion on the following spectrum to see if it satisfies the criterion or not?
The Nyquist criterion for avoiding intersymbol interference (ISI) requires the pulse to have zeros at multiples of the symbol interval $T$, such that symbols do not interfere with each other. The time domain requirement is

$$h(t)=\begin{cases}1,&amp;t=0\\0,&amp;t=nT\end{cases}\tag{1}$$

In the frequency domain, criterion $(1)$ can be formulated as

$$\sum_{k=-\infty}^{\infty}H\left(f-\frac{k}{T}\right)=T\tag{2}$$

where $H(f)$ is the Fourier transform of $h(t)$. I.e., the shifted spectra (shifted by the symbol rate) must add up to a constant.

I leave it up to you to decide whether or not the given pulse satisfies $(1)$ and $(2)$.

I suggest you go through your lectures notes because it would be surprising if the Nyquist criterion has never been mentioned and you get an exercise like this.