the elements iron and oxygen can react to form the compound iron oxide. What type of reaction is this? Explain?

Some general reaction types that you should memorize
.. (1).. A + B ---> AB.. .. . ... .. .. .... .. .. synthesis
.. (2).. AB ----> A + B.. . .... ... .. .... .. .. decomposition
.. (3).. AB + C ---> AC + B.. .. ... ... .. ...single replacement
.. (4).. AB + CD ----> AD + CB.. . .. .. ..double replacement
.. (5).. CxHy + O2 ---> CO2 + H2O.. . .combustion

REDOX reactions.. . .REDuction OXidation are special case of those reactions where 1 atom is reduced in oxidation state and other is increased in oxidation state

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your reaction
.. Fe + O2 ---> FexOy
for this reaction..
.. the Fe on the left is in the 0 oxidation state
.. the Fe on the right is in the +(2y/x) oxidation state
.. the O on the left is in the 0 oxidation state
.. the O on the right is in the -2 oxidation state
meaning
.. the O is reduced... . . (it's reduced in oxidation state)
.. the Fe is oxidized.. . .(oxidation state increased)
this is a REDOX reaction

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AND.. it's also a synthesis reaction.. (aka combination reaction)

oxidation (or oxidation/reduction) reaction
also called a combination reaction

Oxidation/reduction reaction