A plausible explanation of the difference between Genesis 1 and 2 is that they reflect two different earlier creation stories which the writer (Moses) of Genesis recorded, one that does not contain the Adam/Eve story and one that does. The bible is written by many different people, in different times and often do reflect older stories and tales as I have outlined on other pages on the website.
Genesis 1 King James Version (KJV)
27 So God created man in his own image, in the image of God created he him; male and female created he them.
28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
29 And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat.
30 And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so.
31 And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.
Genesis 2 King James Version (KJV)
1 Thus the heavens and the earth were finished, and all the host of them.
2 And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made.
3 And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made.
4 These are the generations of the heavens and of the earth when they were created, in the day that the Lord God made the earth and the heavens,
5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the Lord God had not caused it to rain upon the earth, and there was not a man to till the ground.
6 But there went up a mist from the earth, and watered the whole face of the ground.
7 And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
8 And the Lord God planted a garden eastward in Eden; and there he put the man whom he had formed.
Genesis 6 King James Version (KJV)
6 And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,
2 That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.
3 And the Lord said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.
4 There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
5 And God saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
6 And it repented the Lord that he had made man on the earth, and it grieved him at his heart.
7 And the Lord said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them.