Let $ABC$ be a triangle such that $|AB|=8$ and $|AC|=2|BC|$. What is the largest value of altitude from side $[AB]$?

$
\textbf{(A)}\ 3\sqrt 2
\qquad\textbf{(B)}\ 3\sqrt 3 
\qquad\textbf{(C)}\ 5
\qquad\textbf{(D)}\ \dfrac {16}3
\qquad\textbf{(E)}\ 6
$
1. Let \( K \) be a point on \( [AC] \) such that \( \angle KBC = \angle CAB \). Then \( \triangle CKB \sim \triangle CBA \).
2. Let \( BC = 2x \). Then \( AC = 4x \).
3. Using the similarity of triangles:
   \[
   \frac{BK}{AB} = \frac{CK}{BC} = \frac{BC}{AC} = \frac{1}{2}
   \]
   So \( BK = 4 \) and \( CK = x \).
4. The area of \( \triangle ABC \) is:
   \[
   [ABC] = \frac{1}{2} \times AB \times h = 4h
   \]
5. To maximize \( h \), we use the fact that the maximum area occurs when the altitude is maximized:
   \[
   h_{\text{max}} = \frac{64}{12} = \frac{16}{3}
   \]

The final answer is \(\boxed{\frac{16}{3}}\)