First; use the relationship of molarity and moles/liter to find the moles of the solution.
so 0.600M ×0.030L = 0.018 moles
Then use the mole to mole ratio of lithium to lithium carbonate
0.18 × (2 Li ÷1 Li2CO3) = 0.036
and then multiply by Avogadro's number to find the ions of lithium
0.036 moles × (6.022×10^{23} ) = 2.167 ×10∧22 ions Li