Solution
= Solution
The equations $3m=4l$ and $2n=5k$ are equivalent to
$$
m=4r,
\quad l=3r,
\qquad
n=5s,
\quad k=2s
$$
for nonnegative integers $r,s$. Hence the language is
$$
\{a^{4r}b^{5s}c^{2s}d^{3r}:r,s\geq0\},
$$
which is the <nested two-pair count language> generated by
$$
S\to aaaaSddd\mid T,
\qquad
T\to bbbbbTcc\mid\epsilon.
$$
It is therefore context-free.