The c.d.f. $F(x)=P(X\leq x)$ is built by adding up probabilities from the smallest value onward; once the full table is built, $P(2<X\leq4)$ can be read off directly as $F(4)-F(2)$. …

Step 1 — build the c.d.f. by cumulative addition:

Note that $F(4)=1$, as required, since $X$ is certain to be at most its largest value, and $F(x)$ rises steadily (never falls) as $x$ increases, exactly as a valid c.d.f. must.

Step 2 — find $P(2 < X \leq 4)$ using the c.d.f. subtraction rule:

$P(2 < X \leq 4) = F(4) - F(2) = 1.0 - 0.4 = 0.6$ …

The direct route — simply adding $p_3+p_4$ — is used above as the cross-check; either method is acceptable, but the c.d.f.-subtraction method becomes far quicker once the full c.d.f. table is already availabl …

A common error is including $X=2$ in the range $2<X\leq4$ (treating it as $2\leq X\leq4$) which would wrongly add $p_2$ as well — always read the inequality symbols careful …