The current area of the garden is 6 x 4 = 24 yd². Doubling the area would result in an area of 48 yd². If he is going to increase each side by the same amount, let's call that amount x. We have the following equation:
(6 + x)(4 + x) = 48
24 + 10x + x² = 48
x² + 10x - 24 = 0
(x - 2)(x + 12) = 0
The only logical solution is x = 2 since dimensions cannot be negative. Therefore, each dimension must be increased by 2 yd. If we do, we see that the new dimensions of the garden will be 8 x 6 = 48 yd², which is double the original area of the garden.