An integer is divisible by $18$ if and only if the sum of its digits is divisible by $9$ and the last digit is even (meaning it is divisible by both 9 and 2).  The sum of the digits of $-11213141$ is 14.  Since $-11213141$ is negative, this number is 5 $\textit{less than}$ a multiple of 9.  The number is 4 $\textit{more than}$ a multiple of 9.  Subtracting 4 gives  \[-11213141 = -11213145+4.\]Since $-11213145$ has a digit sum of 18, this number is a multiple of 9.  However this is not a multiple of 18 so we need to subtract 9 again: \[-11213141 = -11213154+13.\]Now the number $-11213154$ is a multiple of 18, so the answer is $\boxed{13}$. $$-11213141\equiv 13\pmod {18}.$$
Question:
What integer $n$ satisfies $0\le n<18$ and $$n\equiv -11213141\pmod{18}~?$$
Answer:
Let's think step by step.

user
13
What integer $n$ satisfies $0\le n<18$ and $$n\equiv -11213141\pmod{18}~?$$
test