What is the next term of the geometric sequence?

To find the next term of the geometric sequence given by

\[
-\dfrac{128}{27},\ \dfrac{32}{9},\ -\dfrac{8}{3},
\]

we first need to determine the common ratio of the sequence.

The second term divided by the first term gives us the common ratio \( r \):

\[
r = \frac{\frac{32}{9}}{-\frac{128}{27}}.
\]

To simplify this, we multiply by the reciprocal of the first term:

\[
r = \frac{32}{9} \cdot \left(-\frac{27}{128}\right).
\]

Calculating this gives:

\[
r = -\frac{32 \cdot 27}{9 \cdot 128}.
\]

Now simplify \(-\frac{32}{128}\) (which is \(-\frac{1}{4}\)) and \(\frac{27}{9}\) (which is \(3\)):

\[
r = -\frac{1 \cdot 3}{4} = -\frac{3}{4}.
\]

Next, we can verify this common ratio by checking the third term divided by the second term:

\[
\frac{-\frac{8}{3}}{\frac{32}{9}} = -\frac{8}{3} \cdot \frac{9}{32} = -\frac{8 \cdot 9}{3 \cdot 32}.
\]

Calculating \( -\frac{8}{32}\) (which simplifies to \(-\frac{1}{4}\)) and \(\frac{9}{3}\) (which is \(3\)) gives:

\[
-\frac{3}{4}.
\]

The common ratio \( r \) is confirmed as \(-\frac{3}{4}\).

To find the next term \( a_4 \), we multiply the third term by the common ratio:

\[
a_4 = a_3 \cdot r = -\frac{8}{3} \cdot -\frac{3}{4}.
\]

Calculating this results in:

\[
a_4 = \frac{8 \cdot 3}{3 \cdot 4} = \frac{8}{4} = 2.
\]

Thus, the next term in the geometric sequence is

\[
\boxed{2}.
\]