Given,

Mass of carbon dioxide = 4.4 g

Molar mass of carbon dioxide= 44g/mol

Mass of methane = 3.2g

Molar mass of methane = 16g/mol

Now amount of methane, n_{CH4} = 3.2/ 16 = 0.2 mol

& amount of CO_{2} n_{CO2} = 4.4/ 44 = 0.1 mol

Also we know ,

Pv = (n_{CH4 }+ n_{CO2}) RT

OR P X 9 = (0.2 +0.1) x 0.0821 x 300

Or p = 0.3 x 0.0821 x 300 / 9 = 0.82 atm

Hence, the total pressure exerted by the mixture is 0.82 atm