1. **State the problem:** We need to find two consecutive even integers whose difference of squares is 68. 2. **Define variables:** Let the first even integer be $x$. Since the integers are consecutive even numbers, the next integer is $x+2$. 3. **Write the equation:** The difference of their squares is given by $$ (x+2)^2 - x^2 = 68 $$ 4. **Expand the squares:** $$ (x+2)^2 = x^2 + 4x + 4 $$ So, $$ (x^2 + 4x + 4) - x^2 = 68 $$ 5. **Simplify the equation:** $$ 4x + 4 = 68 $$ 6. **Solve for $x$:** $$ 4x = 68 - 4 $$ $$ 4x = 64 $$ $$ x = \frac{64}{4} = 16 $$ 7. **Find the two integers:** First integer: $16$ Second integer: $16 + 2 = 18$ 8. **Verify the solution:** $$ 18^2 - 16^2 = 324 - 256 = 68 $$ which matches the problem statement. **Final answer:** The two consecutive even integers are $16$ and $18$.