INDEPENDENCIA Y LIBERTAD means Independence and Liberty on your old 1/4 real coin from the State of Durango (Estado de Durango) in Northern Mexico. It seems there is renewed interest in collecting old coins from the various state-run mints of Mexico, and that drives up value. There are hundreds of unique types of these interesting coins, and that challenges collectors to assemble a complete set.
The term real, pronounced roughly ray-al, is the denomination of the coin. Before Mexico went to its modern decimal system, i.e., 100 centavos in one peso, the real denomination was issued in multiples of two, like this: 1/8 real, 1/4 real, 1/2 real, 1 real, 2 reales, 4 reales, and 8 reales. The 8 reales coins were big and heavy, like a silver dollar. They became famous as 'pieces of 8' in early Americana.
Most of these old state-minted coins are crudely made and heavily worn. The coin in the picture fits the 'crude' and 'worn' description, but it would still sell retail for $20 US dollars or so. A specimen in better condition would easily double that value, or more.
Dealers usually pay about one-half of retail for coins they buy from the general public. If Suzy wants to sell her coin to a dealer, and if Suzy's coin looks about like our picture, a dealer would probably pay about $10.