As usual it helps to try a simpler problem first, maybe $4$ or $5$ units. How many patterns are there that start with S? How many with L?

For $4$ units, there are $5$ patterns:

SSSS

SSL

SLS

LSS

LL

For $5$ units there are $8$ patterns:

SSSSS

SSSL

SSLS

SLSS

SLL

LSSS

LSL

LLS

There are $5$ starting with S and $3$ starting with L. If a $5$-unit pattern starts with S, there are $4$ units left to fill. We already know that there are $5$ patterns that last $4$ units, so it makes sense that there are $5$ patterns starting with S. The patterns that start with L have $3$ units left to fill, so there are $3$ of them (the number of $3$-unit patterns).

Now we have a quick way to work it out. For patterns lasting $6$ units, there are $8$ starting with S and $5$ starting with L, for a total of $13$. For $7$ units, $13 + 8 = 21$ patterns. This is the Fibonacci sequence (first explored in Question 3.1.4), where every term is found by adding the previous two.

Units	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
Patterns	$1$	$2$	$3$	$5$	$8$	$13$	$21$	$34$	$55$	$89$	$144$

Hence there are $144$ patterns of syllables with a duration of $11$ units.