Las instrucciones de lavado explican el programa de lavado.

Because instrucción is a feminine noun in Spanish. Its singular form is la instrucción, so the plural is las instrucciones.

A quick pattern:

• la instrucción = the instruction
• las instrucciones = the instructions

The article has to match the noun in gender and number.

Because the subject is las instrucciones, which is plural. In Spanish, verbs must agree with the subject.

• la instrucción explica = the instruction explains
• las instrucciones explican = the instructions explain

So explican is the third-person plural form of explicar.

De lavado means of washing or more naturally in English, washing / wash depending on context.

In this sentence:

• instrucciones de lavado = washing instructions / wash instructions / laundry instructions
• programa de lavado = washing program / wash cycle / laundry program

Spanish often uses de + noun where English might use:

• a noun used like an adjective, or
• a compound noun

So instead of something like washing instructions formed directly, Spanish says instructions of washing structurally: instrucciones de lavado.

Good question. Although many Spanish nouns ending in -a are feminine, programa is one of the common exceptions and is masculine.

So:

• el programa
• los programas

Other similar masculine nouns of Greek origin include:

• el problema
• el sistema
• el tema

So the article el is correct here.

Here lavado is being used as a noun, meaning something like washing or wash.

Compare:

• lavar = to wash
• lavado = washing / wash

After de, Spanish often uses a noun:

• instrucciones de lavado
• programa de lavado

Using de lavar here would not sound natural in this context.

Because the sentence is saying that the instructions explain the washing program.

So:

• there are multiple instructions → las instrucciones
• there is one program/cycle being referred to → el programa

Spanish does not need both nouns to match in number. Each noun just reflects what it refers to.

Yes, functionally it is describing the noun, even though grammatically it is a prepositional phrase.

For example:

• instrucciones de lavado describes what kind of instructions
• programa de lavado describes what kind of program

English often uses adjectives or noun modifiers:

• washing instructions
• washing program

Spanish commonly uses de + noun for this job.

Not with exactly the same meaning.

• instrucciones de lavado = washing instructions / laundry instructions
• instrucciones para lavar = instructions for washing

The second version sounds more like instructions telling you how to wash something. The original phrase sounds more like the standard label or category name you might see on clothing or appliances.

So de lavado is the more natural choice for this kind of general label.

Spanish often leaves out possessives when the meaning is clear from context. The sentence simply says:

• Las instrucciones de lavado explican el programa de lavado.

This is more neutral and general. English sometimes adds words like its or the machine’s, but Spanish often does not unless it is necessary for clarity.

The structure is:

Subject + verb + direct object

• Las instrucciones de lavado = subject
• explican = verb
• el programa de lavado = direct object

So literally:

• The washing instructions explain the washing program.

This is a very normal Spanish word order.

Usually, no, not in standard natural Spanish for this sentence.

Spanish uses definite articles much more often than English:

• las instrucciones
• el programa

Leaving them out would sound incomplete or unnatural in most contexts.

The form lavado can be either:

• a past participle of lavar = washed
• a noun = washing / wash

Here it is a noun because it appears in the phrase de lavado, where it names a type or category:

• instructions of washing
• program of washing

If it were a participle, it would usually be connected to a verb like haber or estar, or it would clearly describe a noun:

• he lavado = I have washed
• la ropa lavada = the washed clothes

So in this sentence, it is best understood as a noun.