Harold has a photograph that is 8in x 10in. that he wants to print at a reduced size to fit into a frame that is 6in. tall. what will be the dimensions of the new photograph?

Depends on the height of the photograph.  It doesn't say whether 8in or 10 in is the height, so I'll answer for both.

   If the original height was 8in, the new dimensions would be 6in tall and 7.5 inches wide.

  If the original height was 10in, the new dimensions would be 6 inches tall and 4.8 inches wide.

Step-by-step explanation:

*In either case we will use proportions to solve.  

    a/b = c/d        where a is the original height, b is the original width, c is the new height of 6in, and d is the new width

  We are given a and b (the original dimensions), and need to find d.  

If the original height was 8in:  Here, a = 8, and b = 10 (original dimensions)                                                    

                                                  We know c = 6, so set up the proportions and    

                                                   solve for d

         8/10 = 6/d        (solve this by using cross multiplication)

          8d = 60            (now solve for d)

         d = 60/8

                          d = 7.5

  The new dimensions are  6in tall and 7.5 inches wide.

If the original height was 10in:  Here, a = 10, and b = 8 (original dimensions)                                                    

                                                  We know c = 6, so set up the proportions and    

                                                   solve for d

         10/8 = 6/d        (solve this by using cross multiplication)

          10d = 48            (now solve for d)

         d = 48/10

                          d = 4.8

  The new dimensions are  6 inches tall and 4.8 inches wide.