In the diagrams below:
H = hero, ABCD = spaces covered by large monster, + = empty space, X = some other LoS obstruction (rubble, wall, another hero, etc.)
In the example from p.10 of the JitD rules, the hero has line of sight to the closer half (AB) of the monster (an ogre, in the rulebook example) but does not have LoS to the far half. The hero can attack the monster but could not target a blast on the far half (CD) of the monster.
H+
AB
CD
However, if we change the scenario a bit, it gets more interesting:
+++H
ABX+
LoS from H to B is blocked by the obstruction in X.
LoS from H to A is blocked by the figure in B.
RaW, H does not appear to have LoS to space B or space A. But is that really the intent? Does the monster completely block LoS to itself?
1. Can the hero attack a large monster in AB?
2. Can the hero target space A or space B? (probably only matters with a blast weapon)
3. Can the monster make a ranged (non-breath, etc) attack against the hero?
4. If A and B are different small monsters, can the hero target either?
RaW, I believe the answers are 1-no, 2-n/a, 3-no, 4-no. However, it seems odd that you cannot attack a hellhound because the hellhound itself is in the way of your shot.