Step 1: Identify the unknowns from the clues.
White phosphorus reacts with sulphuryl chloride to give a solid A and a gas D. Heating A gives an oily liquid X and a gas C. We need the shape of X.
Step 2: Track the chemistry to find X.
The reaction route leads to phosphorus chloride chemistry. The oily, colourless liquid formed here is phosphorus trichloride, $PCl_3$. So X is $PCl_3$.
Step 3: Count the electron pairs on phosphorus.
In $PCl_3$ the central phosphorus has $5$ valence electrons. Three are used to bond three chlorine atoms, leaving one lone pair. So there are $3$ bond pairs and $1$ lone pair.
Step 4: Apply VSEPR.
Four electron domains arrange in a tetrahedral direction, but one corner is a lone pair, not an atom. So the shape of the atoms is not a full tetrahedron.
Step 5: Find the molecular shape.
With three bonded atoms and one lone pair, the molecule takes a pyramidal (trigonal pyramidal) shape, much like ammonia.
Step 6: State the answer.
The shape of X ($PCl_3$) is pyramidal.
\[ \boxed{\text{Pyramidal}} \]