A number has 3 digits. When it is divided by 6 or 7, it leaves a remainder if 1. When it is divided by 8 or 11, it leaves a remainder of 7.
What is the largest of such number?
One method: Start at the high end of the three-digit numbers: 999, 998, 997, etc.
Since the number is not evenly divisible by 6, it cannot be evenly divisible by 2 or 3, so start eliminating these values.
Since the number has a remainder of 7 when divided by 8, it is one less than a multiple of 8, so start marking those and then listing the values one less.
(You don't say at what level you are studying, so, other than working further on the above list, I hesitate to recommend any particular other techniques.)
Give yourself some time, and have fun!