To solve $[69 \cdot 13] \mod 4$:

1. First, calculate $69 \cdot 13$:

$69 \cdot 13 = 897$

2. Now, find $897 \mod 4$. To do this, divide 897 by 4 and take the remainder:

$897 \div 4 = 224 \text{ remainder } 1$

Thus, $897 \mod 4 = 1$.

The result is:

$[69 \cdot 13] \mod 4 = 1$

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What is $[85 \cdot 23] \mod 7$?
2. Find $[120 \cdot 15] \mod 6$.
3. Simplify $[45 \cdot 33] \mod 5$.
4. Calculate $[250 \cdot 19] \mod 9$.
5. Determine $[39 \cdot 72] \mod 8$.

Tip: When calculating large modular products, it's often easier to reduce each number modulo first before multiplying.