$I)\ \{a^mb^nc^pd^q \mid m+p=n+q, \text{ where } m, n, p, q \geq 0 \}$
Grammar :
$S \longrightarrow aSd\ |\ ABC\ |\in$
$A \longrightarrow aAb\ |\ ab\ |\in $
$B \longrightarrow bBc\ |\ bc\ |\in$
$C \longrightarrow cCd\ |\ cd\ |\in $
Above Grammar is CFG so it will generate CFL.
$II)\ \{a^mb^nc^pd^q \mid m=n \text{ and }p=q, \text{ where } m, n, p, q \geq 0 \}$
Grammar :
$S \longrightarrow AB\ |\in $
$A \longrightarrow aAb\ |\ ab$
$B \longrightarrow cBd\ |\ cd$
Above Grammar is CFG so it will generate CFL.
$III)\ \{a^mb^nc^pd^q \mid m=n =p \text{ and } p \neq q, \text{ where } m, n, p, q \geq 0 \}$
More than one comparison so NOT CFL.
$IV)\ \{a^mb^nc^pd^q \mid mn =p+q, \text{ where } m, n, p, q \geq 0 \}$
It is CSL but NOT CFL.
Correct Answer: $B$