Generally, the shared secret
DHKey is the first coordinate of the $b$th multiple of the point $A$, denoted $[b]A$.
Here, $b$ represents B's private key
Private B and $A$ is A's public key
Using the computer algebra package sage, this can be computed as follows. First, we set up the NIST curve P-192 (the constants can be found online):
sage: p = 6277101735386680763835789423207666416083908700390324961279
sage: b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
sage: E = EllipticCurve(Zmod(p), [0, 0, 0, -3, b])
Then, we plug in the given values and compute $Q:=[b]A$:
sage: b = 0x1e636ca790b50f68f15d8dbe86244e309211d635de00e16d
sage: Ax = 0x15207009984421a6586f9fc3fe7e4329d2809ea51125f8ed
sage: Ay = 0xb09d42b81bc5bd009f79e4b59dbbaa857fca856fb9f7ea25
sage: Q = b * E(Ax, Ay)
...yielding the desired value:
If you want to perform this computation in a different environment (other programming languages, etc.), I am sure you will find plenty of implementations for point multiplication on P-192 using your favourite internet search engine.