To find the largest 4-digit number divisible by 88, we first divide the largest 4-digit number, 9999, by 88:
\[ 9999 \div 88 = 113.625 \]
Taking the integer part of the quotient, we get 113. Now, multiply 113 by 88 to get the largest multiple of 88 that is less than or equal to 9999:
\[ 88 \times 113 = 9944 \]
Thus, the largest 4-digit number divisible by 88 is 9944.