In ∆ ABC, DE|| BC and 5 AE = 3EC. If AB = 6.4 units, then the value of DB (in units) is:

The correct option is 4.

Let us analyze the problem step-by-step using the basic proportionality theorem (Thales's theorem).

We are given a triangle $ABC$ where a line segment $DE$ is parallel to the side $BC$. Here, point $D$ lies on the side $AB$ and point $E$ lies on the side $AC$.

According to the basic proportionality theorem, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio. Therefore, we have:
$\frac{AD}{DB}=\frac{AE}{EC}$

We are given the relationship between the segments on the side $AC$:
$5AE=3EC$
This can be rewritten to find the ratio:
$\frac{AE}{EC}=\frac{3}{5}$

Since the ratios are equal, we also have:
$\frac{AD}{DB}=\frac{3}{5}$

Let $AD=3x$ and $DB=5x$ for some positive constant $x$.

The total length of the side $AB$ is the sum of $AD$ and $DB$:
$AB=AD+DB=3x+5x=8x$

We are given that $AB=6.4$ units. Thus, we can solve for $x$:
$8x=6.4$
$x=\frac{6.4}{8}=0.8$

Now, we can find the value of $DB$:
$DB=5x=5\times 0.8=4$ units.