To find the limit of the expression, we can simplify it first.

First, let's expand the numerator:
(3n^3 + 2)(4n + 1)^2 = (3n^3 + 2)(16n^2 + 8n + 1)
= 48n^5 + 24n^4 + 3n^3 + 32n^3 + 16n^2 + 2

Next, let's expand the denominator:
(2n^2 + 1)(3n^3 - 7) = 6n^5 - 14n^2 + 3n^3 - 7

Now, let's simplify the expression:
lim (3n^3 + 2)(4n + 1)^2/((2n^2 + 1)(3n^3 - 7))
= lim (48n^5 + 24n^4 + 3n^3 + 32n^3 + 16n^2 + 2)/(6n^5 - 14n^2 + 3n^3 - 7)

As n approaches infinity, the highest power of n in the numerator and denominator is n^5. Therefore, we can ignore the lower order terms in the numerator and denominator.

lim (48n^5 + 24n^4 + 3n^3 + 32n^3 + 16n^2 + 2)/(6n^5 - 14n^2 + 3n^3 - 7)
= lim (48n^5)/(6n^5)
= lim 8
= 8

Therefore, the limit of the expression is 8.