Answer
\[
(K \circ H)(0) = 0,\quad
(K \circ H)(1) = 2,\quad
(K \circ H)(2) = 0,\quad
(K \circ H)(3) = 2.
\]
Work Step by Step
We have two functions on the integers:
1. \(H(a) = 6a.\)
2. \(K(a) = a \bmod 4.\)
Thus,
\[
(K \circ H)(x) \;=\; K\bigl(H(x)\bigr) \;=\; K\bigl(6x\bigr) \;=\; 6x \bmod 4.
\]Evaluate this for \(x = 0,1,2,3\):
1. \((K \circ H)(0) = 6 \cdot 0 \bmod 4 = 0.\)
2. \((K \circ H)(1) = 6 \cdot 1 \bmod 4 = 6 \bmod 4 = 2.\)
3. \((K \circ H)(2) = 6 \cdot 2 \bmod 4 = 12 \bmod 4 = 0.\)
4. \((K \circ H)(3) = 6 \cdot 3 \bmod 4 = 18 \bmod 4 = 2.\)
