Twelve towels

I had twelve wet towels and one washing line. The line holds six towels, and a towel in the sun dries in two hours.

$12$ wet towels, $1$ line. The line holds $6$; a towel dries in $2$ h.

Towels $n$, lines $L$, time $t$: $6$ per line, $2$ h per round.

Six towels first, then six more: two hours, then two hours again. Four hours in all, and the sun would be gone by then.

$6$ first, then $6$ more: $2+2=4$ h. The sun is gone by then.

$t=2\lceil \frac{12}{6\times 1}\rceil =4$ for $L=1,n=12$.

So I tied a second line from the window to the tree. Now all twelve towels hung together and all of them dried in two hours.

A second line: $2\times 6=12$ places, so all $12$ towels dry together in $2$ h.

$t=2\lceil \frac{12}{6\times 2}\rceil =2$ for $L=2$.

Then I found a thirteenth towel under the bed. Thirteen towels do not fit on two lines, so one has to wait for a second round: four hours again. One towel doubled the time.

Towel number $13$: $13>12$, so a second round is needed, and $2\times 2=4$ h again. One towel doubles the time.

$n=13$: $t=2\lceil \frac{13}{12}\rceil =4$.