Need to write an algebraic expression then simplfy indicating 
the properties used.

This is the problem:
four times the sum of a and b increased by twice the sum of a and 2b
Thanks

-------------------------------------------------------------------

          Four times the sum of a and b increased by twice the sum of a and 2b

Replace the words "the sum of a and 2b" by "(a + 2b)"

          Four times the sum of a and b increased by twice (a + 2b)

Replace "twice (a + 2b)" by "2(a + 2b)"

          Four times the sum of a and b increased by 2(a + 2b)

Replace the words "the sum of a and b" by "(a + b)

          Four times (a + b) increased by 2(a + 2b)

Replace "Four times (a + b)" by 4(a + b)

          4(a + b) increased by 2(a + 2b)

Replace the words "increased by" by a plus sign " + "

          4(a + b) + 2(a + 2b)

That's the algebraic expression.  Now we simplify it.
Remove the parentheses using the distributive principle:

          4a + 4b + 2a + 4b

Combine the 4a and 2a, getting 6a and combine the 4b and the 4b,
getting 8b:

          6a + 8b

Edwin