2 of her lambs had 2 babies each so that adds 2*2 = <<2*2=4>>4 lambs
She starts with 6 and adds 4 baby lambs so she had 6+4 = <<6+4=10>>10 lambs
She traded 3 of those lambs for a goat so she has 10-3 =<<10-3=7>>7 lambs
She has 7 and woke up to find 7 more lambs in the field so she has a total of 7+7 = <<7+7=14>>14 lambs
#### 14