Compound F
This is a white crystalline compound which gives a yellow-green flame colour. On heating the solid strongly it melts and gives off a brown gas. The gas relights a glowing splint.
The yellow-green flame test suggests a barium salt. The gas which relights a glowing splint is oxygen. The brown gas will be nitrogen dioxide. The production of nitrogen dioxide and oxygen gases on heating indicates a group 2 or transition metal nitrate.
Answer: barium nitrate.
You can find out more about heating the nitrates here. A nitrate could have been confirmed with the brown ring test.