To solve this problem, we need to identify which palindromic base sequence of DNA can be easily cut by a particular restriction enzyme.$\newline$Restriction enzymes typically recognize specific palindromic sequences in DNA and cut at those sites.$\newline$Let's analyze each option:$\newline \bullet$Option 1: 5'-GATACT-3' ; 3'-CTATGA-5'$\newline$ - This sequence is not a typical recognition site for common restriction enzymes.$\newline \bullet$Option 2: 5'-GAATTC-3' ; 3'-CTTAAG-5'$\newline$ - This sequence is recognized by the restriction enzyme EcoRI, which cuts between G and A, producing sticky ends.$\newline$ - It is a well-known palindromic sequence that is easily cut by EcoRI.$\newline \bullet$Option 3: 5'-CTCAGT-3' ; 3'-GAGTCA-5'$\newline$ - This sequence is not a typical recognition site for common restriction enzymes.$\newline \bullet$Option 4: 5'-GTATTC-3' ; 3'-CATAAG-5'$\newline$ - This sequence is not a typical recognition site for common restriction enzymes.$\newline$Based on the analysis, Option 2 is the correct answer as it contains the sequence recognized by EcoRI.$\newline$Therefore, the correct option is Option 2.