Step 1: Numbers with remainder 2 when divided by 3 are of the form $3k + 2$. Step 2: Numbers with remainder 2 when divided by 4 are of the form $4m + 2$. Step 3: Find the LCM of 3 and 4. LCM(3, 4) = 12 Step 4: Numbers satisfying both conditions are of the form $12n + 2$. Step 5: Verification: $2 \div 3 = 0$ remainder $2$, $2 \div 4 = 0$ remainder $2$ $14 \div 3 = 4$ remainder $2$, $14 \div 4 = 3$ remainder $2$

Answer: Numbers that satisfy both conditions are 2, 14, 26, 38, 50, 62, ... The algebraic expression for all such numbers is $12n + 2$, where $n$ is any non-negative integer.