To solve the given expression \((\frac{15}{11} - \frac{4}{13}) \cdot \frac{12}{17} + (\frac{7}{11} - \frac{9}{13}) \cdot \frac{12}{17}\), we can follow these steps:

1. Simplify the fractions inside the parentheses.
2. Multiply the simplified fractions by \(\frac{12}{17}\).
3. Add the results.

Let's start with the first part: \(\frac{15}{11} - \frac{4}{13}\).

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 11 and 13 is 143.

\[
\frac{15}{11} = \frac{15 \cdot 13}{11 \cdot 13} = \frac{195}{143}
\]
\[
\frac{4}{13} = \frac{4 \cdot 11}{13 \cdot 11} = \frac{44}{143}
\]

Now, subtract the fractions:

\[
\frac{195}{143} - \frac{44}{143} = \frac{195 - 44}{143} = \frac{151}{143}
\]

Next, multiply by \(\frac{12}{17}\):

\[
\left(\frac{151}{143}\right) \cdot \frac{12}{17} = \frac{151 \cdot 12}{143 \cdot 17} = \frac{1812}{2431}
\]

Now, let's simplify the second part: \(\frac{7}{11} - \frac{9}{13}\).

Again, we need a common denominator, which is 143.

\[
\frac{7}{11} = \frac{7 \cdot 13}{11 \cdot 13} = \frac{91}{143}
\]
\[
\frac{9}{13} = \frac{9 \cdot 11}{13 \cdot 11} = \frac{99}{143}
\]

Now, subtract the fractions:

\[
\frac{91}{143} - \frac{99}{143} = \frac{91 - 99}{143} = \frac{-8}{143}
\]

Next, multiply by \(\frac{12}{17}\):

\[
\left(\frac{-8}{143}\right) \cdot \frac{12}{17} = \frac{-8 \cdot 12}{143 \cdot 17} = \frac{-96}{2431}
\]

Finally, add the two results:

\[
\frac{1812}{2431} + \frac{-96}{2431} = \frac{1812 - 96}{2431} = \frac{1716}{2431}
\]

So, the simplified result of the given expression is:

\[
\frac{1716}{2431}
\]

This fraction can be simplified further if there are common factors between the numerator and the denominator. However, in this case, 1716 and 2431 do not have any common factors other than 1, so the fraction is already in its simplest form.