Given these sets:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6, 7}
C = {3, 5, 7, 9}

List the elements of this set
A ∩ (B U C) 

Substitute the sets for the letters:

    A     ∩ [     B      U     C    ]
    |             |            |  
{1,2,3,4} ∩ [{3,4,5,6,7} U {3,5,7,9}]

We do the part in [ ] first.  To take the union of {3,4,5,6,7} and {3,5,7,9}
and make a set with elements that are in one or the other or both. So
we replace the bracketed expression by {3,4,5,6,7,9}

    A     ∩ [     B      U     C    ]
    |             |            |  
{1,2,3,4} ∩ [{3,4,5,6,7} U {3,5,7,9}]

{1,2,3,4} ∩ [     {3,4,5,6,7,9}]

and that is just

      {1,2,3,4} ∩ {3,4,5,6,7,9}

To take the intersection we may use ONLY elements which are in common
to both sets.  So the final answer is

              {3,4}

because 3 and 4 are the only elements in common to both sets.

Edwin