Finding order of acidic strength for given compounds
Here, this was a simple question of checking the most acidic compound out of the four and this would have given you the answer. $\ce{H2O}$ will be most acidic as the negative charge will be formed on an oxygen compared to nitrogen and carbon in the other two cases.
However, the interesting question here is the part in the middle, what about $\ce{C2H2}$ and $\ce{Ph3CH}$? Which is more acidic?
If you take a look at the $\mathrm p K_\mathrm a$ values of the given compounds, you would notice that the values would come out to be:
\begin{array}{l|c}
\hline
\text{Compound} &amp;\mathrm {p}K_\mathrm {a} \\
\hline
\ce{H2O} &amp; 15.7 \\
\ce{NH3} &amp; 38\\
\ce{C2H2} &amp; 24\\
\ce{Ph3CH} &amp; 31.5 \\
\hline
\end{array}
Now, this is the definitive set of values which states the order should be  $\ce{H2O &gt; C2H2 &gt; Ph3CH &gt; NH3}$.

Note: Next part is speculative as I do not have a solid reason for $\mathrm pK_\mathrm a$ values being so for acetylene and the triphenyl system.
A question that may arise at this point is why is this so? Why would a triphenyl system with $3$ phenyl rings be less acidic than acetylene? What about the three rings providing resonance?
This is because in reality, only one phenyl ring provides resonance at a time. Due to the size of phenyl groups, the structure is not fully planar. Another reasoning is that the negative charge lies on an $\mathrm{sp^3}$ carbon whereas in acetylene it is on an $\mathrm{sp}$ carbon.