In $11$ shown above, take $1$ as carry. Add this $1$ to its left neighbor number $4.$ Thus $4$ becomes $5$
$5\quad 1\quad 9 \quad 6\quad 2\quad 3\quad 5$
Why it works? If you write the numbers in 2 lines (your number on top of 11) and then do a simple multlipication, you will quickly and easily see why this method works for any number no matter how large!
19 * 11 ------ 19 19 ----- 209
The more fun is playing with two numbers having all ones, like: 11111111111111111*11111111111111111 I can give you the answer without writing a single digit down, just by looking at the numbers!