Answer
$a)$ 2 lone pairs of electrons
$b)$ 1 lone pair of electrons
$c)$ 1 lone pair of electrons
$d)$ 2 lone pairs of electrons
Work Step by Step
$a)$ (Oxygen in Dimethyl Ether) The atom has 2 pairs of non-bonding electrons, and we can expect a bent (derived from tetrahedral) geometry for this atom's bonds.
$b)$ (Nitrogen in Trimethyl Amine) The atom has 1 pair of non-bonding electrons, and we can expect a trigonal pyramidal (derived from tetrahedral) geometry for this atom's bonds.
$c)$ (Phosphorus in Phosphine [PH3]) The atom has 1 pair of non-bonding electrons, and we can expect a trigonal pyramidal (derived from tetrahedral) geometry for this atom's bonds.
$d)$ (Sulfur in Methionine) The atom has 2 pairs of non-bonding electrons, and we can expect a bent (derived from tetrahedral) geometry for this atom's bonds.
