A briefcase is a rectangular bag that is most often used by professional workers. Briefcases are usually black and made of leather.
A case is something that goes around something else, for storage and protection. Expensive things that need to be kept safe are usually kept in cases. The picture is of a violin and its case, but it is common to see guitar cases and glasses cases too. Case might also be a word for a situation or the state of things, as in "take some money in case you need it".
To chase is to run after someone or something to try to catch it. The two dogs in the picture are chasing a frisbee.
Embrace is another word for hug, a motion where two people wrap their arms around one another. An embrace is usually a form of affection.
Your face is the front part of your head. Your eyes, nose, mouth, chin and cheeks are all on your face. It is not just humans that have faces. The picture is a gorilla's face.
A fireplace is somewhere, usually indoors, that is built to contain a fire for either cooking or heating. Fireplaces are generally made from brick, stone, rammed earth or any other material that will not burn.
Grace is an English name for girls. Grace means "gracious." The woman in the picture is Grace Kelly.
Lace is a kind of fabric that is made up of loops and holes. Lace usually has flower shapes in it, and is very pretty. It is often found on the edges of dresses.
A mace is a medieval weapon, similar to a club but with an end designed to maximize damage. Some maces simply have a studded ball at the end, others have the ball on a chain. Mace is also a spice, see nutmeg.
A necklace is a pretty piece of jewellery that is worn around the neck. Necklaces are usually made of chain, or a string threaded with beads. Sometimes a pretty pendant is hung from the necklace.