Number Pattern Problem: Matching First and Last Digits in Three-Digit Numbers

Choose a number whose hundreds digit is equal to its units digit.

To determine the correct number, check the digits of each option to see if the hundreds digit equals the units digit:

• Option 1: $644$ - hundreds digit is $6$, units digit is $4$ (they are not equal).
• Option 2: $858$ - hundreds digit is $8$, units digit is $8$ (they are equal).
• Option 3: $677$ - hundreds digit is $6$, units digit is $7$ (they are not equal).
• Option 4: $550$ - hundreds digit is $5$, units digit is $0$ (they are not equal).

Therefore, the number that meets the condition where the hundreds digit equals the units digit is $\textbf{858}$.