1. **State the problem:** We are given two sets defined by functions of $x$ where $x$ is a natural number from 1 to 4. Set $M = \{4x \mid x \in \mathbb{N}, 1 \leq x \leq 4\}$ and set $N = \{8x \mid x \in \mathbb{N}, 1 \leq x \leq 4\}$. We want to find the number of elements in the intersection $M \cap N$. 2. **Write out the elements of each set:** - For $M$: when $x=1,2,3,4$, $M = \{4, 8, 12, 16\}$. - For $N$: when $x=1,2,3,4$, $N = \{8, 16, 24, 32\}$. 3. **Find the intersection $M \cap N$:** - Elements common to both sets are those in both $M$ and $N$. - $M \cap N = \{8, 16\}$. 4. **Count the elements in the intersection:** - There are 2 elements in $M \cap N$. 5. **Answer:** $$n(M \cap N) = 2$$ So, the correct choice is A) 2.