He wanted to make another quilt with an area of 42 square feet. what are its possible dimensions if they must be whole numbers? which length and width makes the most sense for the quilt

Before I start, I wonder if we are missing some information?  The question you posted says "He wanted to make another quilt"...does your question have any information about a first quilt that we need to take into consideration?  

If not, and if this is all the information we have, then you start by knowing that the area of a rectangle (i.e., quilt) = length x width.  So, to get a quilt with an area of 42, you need to find two numbers that multiply together to make 42.  For example, 6 x 7 = 42, so the dimensions of the quilt could be 6 feet by 7 feet.  Technically, 1 x 42 and 2 x 21 and 3 x 14 also = 42, so the quilt dimensions could also be 1 foot by 42 feet or 2 feet by 21 feet or 3 feet by 14 feet, but those would be a really unusual and awkward sizes for a quilt, so 6 feet by 7 feet is the better answer.