We are given these reactants:
H₂SO₄ (aq) + BaCl₂ (aq) ----> ?
BaCl₂ is a soluble salt, so it will dissociate into its ions.
BaCl₂ (aq) ---> Ba²⁺ (aq) + 2 Cl⁻ (aq)
Something similar happens with H₂SO₄, since it is a strong acid it will dissociate into its ions.
H₂SO₄ (aq) ---> 2 H⁺ (aq) + SO₄²⁻ (aq)
Now we can work on the equations. This is a double replacement equation so the molecular equation will be:
H₂SO₄ (aq) + BaCl₂ (aq) ----> 2 HCl (aq) (aq) + BaSO₄ (s)
BaSO₄ is an insoluble salt of Barium, and HCl is a strong acid.
So if we divide the molecular equation in the ions we get the ionic equation:
H₂SO₄ (aq) + BaCl₂ (aq) ----> 2 HCl (aq) (aq) + BaSO₄ (s)
2 H⁺ (aq) + SO₄²⁻ (aq) + Ba²⁺ (aq) + 2 Cl⁻ (aq) ---> 2 H⁺ (aq) + 2 Cl⁻ (aq) + BaSO₄ (s)
And if we cancel out the ions that we have on both sides we get the net ionic equation.
SO₄²⁻ (aq) + Ba²⁺ (aq) ---> BaSO₄ (s)
Answer: First option: SO₄²⁻ (aq) + Ba²⁺ (aq) ---> BaSO₄ (s)