In an experiment, the following four gases were produced $11.2L$  of which two gases at STP will weigh 14g                      

1 mole of any gas at STP must be occupied 22.4 lit of volume.

So, at STP  11.2 L of volume is occupied by 0.5 mol of a gas.

$1{\text{ mole of N}}_{\text{2}}\text{O = 44g}$

$\frac{1}{2}{\text{ mole of N}}_{\text{2}}\text{O = 22g}$

$1{\text{ mole of NO}}_{\text{2}}\text{ = 46}\text{g}$

$\frac{1}{2}{\text{ mole of NO}}_{\text{2}}\text{=}\text{23}\text{g}$

$1{\text{ mole of N}}_2\text{=}\text{28g}$

$\frac{1}{2}{\text{ mole of N}}_2\text{=14g}$

$\text{1 mole of CO = 28g}$

$\frac{1}{2}\text{ mole of CO =14g}$