1. Meaning of electron-deficient molecule

A molecule is called electron deficient if the central atom has less than 8 electrons in its valence shell after bonding, i.e. it has an incomplete octet.

2. Check each given species

(i) $PH_3$

• Phosphorus has 5 valence electrons.
• In $PH_3$, it forms 3 bonds with H and has 1 lone pair.
• Total electrons around P: $3 \times 2 + 2 = 8$
• So, $PH_3$ is not electron deficient.

(ii) $B_2H_6$

• Diborane is a classic electron-deficient molecule.
• Boron has only 3 valence electrons, and in diborane there are bridging $3c$-$2e$ bonds.
• Each boron does not achieve a normal octet through ordinary $2c$-$2e$ bonds.
• Hence, $B_2H_6$ is electron deficient.

(iii) $CCl_4$

• Carbon forms 4 bonds.
• Total electrons around C: $4 \times 2 = 8$
• So, $CCl_4$ is not electron deficient.

(iv) $NH_3$

• Nitrogen has 5 valence electrons.
• In $NH_3$, it forms 3 bonds and has 1 lone pair.
• Total electrons around N: $3 \times 2 + 2 = 8$
• So, $NH_3$ is not electron deficient.

(v) $LiH$

• $LiH$ is essentially an ionic hydride: $Li^+H^-$
• It is not treated as an electron-deficient covalent molecule.
• Hence, $LiH$ is not electron deficient.

(vi) $BCl_3$

• Boron has 3 valence electrons and forms 3 bonds with Cl.
• Total electrons around B: $3 \times 2 = 6$
• Boron has only 6 electrons, so it has an incomplete octet.
• Hence, $BCl_3$ is electron deficient.

3. Count electron-deficient molecules

The electron-deficient molecules are:

• $B_2H_6$
• $BCl_3$

So, the total number is: $2$

4. Correct option

Therefore, the correct option is: $\boxed{C}$