\( B_4H_{10} \) is known as tetrahydroborate, and it contains 3-centre-2-electron bonds in its structure. These bonds are formed by the sharing of electrons between three atoms. In \( B_4H_{10} \), there are two 3-centre-2-electron bonds in each of the four \( B-H \) groups, giving a total of:
\[
\text{Total number of 3-centre-2-electron bonds} = 4 \times 2 = 8.
\]
Thus, the total number of 3-centre-2-electron bonds in \( B_4H_{10} \) is \( \boxed{4} \).