Solution X is aqueous sodium carbonate — colourless. Solution Y is aqueous ammonium iron(II) sulfate — the Fe²⁺ makes it pale green.
Mixing them precipitates iron(II) carbonate — salt Z: a green precipitate forms, and on standing it darkens and turns brown at the surface (oxygen in the air is already oxidising the iron(II) to iron(III)). Filtering leaves the green residue Z on the paper and a colourless filtrate; when the filtrate runs into the dilute sulfuric acid there is effervescence — the gas forms a white precipitate in the limewater → carbon dioxide. The paper's trick: start filtering into the empty tube, and only once no more solid is coming through move the funnel to the acid tube.
Half the moist residue + tilted sulfuric acid (no shaking — watch the fizz around the solid): effervescence → CO₂ → CO₃²⁻; shaking gives a pale yellow solution (part of the residue had already been oxidised to iron(III)). A 1 cm portion + NaOH: a large volume is needed before a green precipitate, insoluble in excess, forms → Fe²⁺, and the mixture becomes warm. So Z = iron(II) carbonate.